Abraham Adrian Albert 1905-1972
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- Bull. Amer. Math. Soc. 80 (1974), 1075-1100
References
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1. Abraham Adrian Albert, Modern Higher Algebra, Univ. of Chicago Press, Chicago, Ill., 1937.
- A. Adrian Albert, Structure of algebras, American Mathematical Society Colloquium Publications, Vol. XXIV, American Mathematical Society, Providence, R.I., 1961. Revised printing. MR 0123587
- A. Adrian Albert, Introduction to Algebraic Theories, University of Chicago Press, Chicago, 1941. MR 0003590 4. Abraham Adrian Albert, College Algebra, McGraw-Hill, New York, 1946; reprinted by Univ. of Chicago Press, Chicago, Ill., 1963. 5. Abraham Adrian Albert, Solid Analytic Geometry, McGraw-Hill, New York, 1949.
- A. Adrian Albert, Fundamental concepts of higher algebra, University of Chicago Press, Chicago, Ill., 1958. MR 0098735
- A. Adrian Albert and Reuben Sandler, An introduction to finite projective planes, Holt, Rinehart and Winston, New York-Toronto, Ont.-London, 1968. MR 0227851
- Studies in modern algebra, Studies in Mathematics, Vol. 2, Mathematical Association of America; distributed by Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0146228 9. Abraham Adrian Albert, A determination of all associative algebras in two, three and four units over a nonmodular field F, M.S. Thesis, University of Chicago, Chicago, Ill., 1927. 10. Abraham Adrian Albert, Algebras and their radicals, and division algebras, Ph.D. Dissertation, University of Chicago, Chicago, Ill., 1928.
- A. Adrian Albert, A determination of all normal division algebras in sixteen units, Trans. Amer. Math. Soc. 31 (1929), no. 2, 253–260. MR 1501481, DOI 10.1090/S0002-9947-1929-1501481-4 12. Abraham Adrian Albert, On the rank equation of any normal division algebra, Bull. Amer. Math. Soc. 35 (1929), 335-338. 13. Abraham Adrian Albert, The rank function of any simple algebra, Proc. Nat. Acad. Sci. U.S.A. 15 (1929), 372-376. 14. Abraham Adrian Albert, On the structure of normal division algebras, Ann. of Math. 30 (1929), 322-338. 15. Abraham Adrian Albert, Normal division algebras in 4p2 units, p an odd prime, Ann. of Math. 30 (1929), 583-590. 16. Abraham Adrian Albert, The structure of an algebra which is a direct product of rational generalized quaternion division algebras, Ann. of Math. 30 (1929), 621-625. 17. Abraham Adrian Albert, On the structure of pure Riemann matrices with non-commutative multiplication algebras, Proc. Nat. Acad. Sci. U.S.A. 16 (1930), 308-312. 18. Abraham Adrian Albert, On direct products, cyclic division algebras, and pure Riemann matrices, Proc. Nat. Acad. Sci. U.S.A. 16 (1930), 313-315.
- A. Adrian Albert, The non-existence of pure Riemann matrices with normal multiplication algebras of order sixteen, Ann. of Math. (2) 31 (1930), no. 3, 375–380. MR 1502951, DOI 10.2307/1968233 20. Abraham Adrian Albert, A necessary and sufficient condition for the non-equivalence of any two rational generalized quaternion division algebras, Bull. Amer. Math. Soc. 36 (1930), 535-540.
- A. Adrian Albert, Determination of All Normal Division Algebras in Thirty-Six Units of Type R$_2$, Amer. J. Math. 52 (1930), no. 2, 283–292. MR 1507918, DOI 10.2307/2370683 22. Abraham Adrian Albert, A note on an important theorem on normal division algebras, Bull. Amer. Math. Soc. 36 (1930), 649-650.
- A. Adrian Albert, New results in the theory of normal division algebras, Trans. Amer. Math. Soc. 32 (1930), no. 2, 171–195. MR 1501532, DOI 10.1090/S0002-9947-1930-1501532-5
- A. Adrian Albert, The integers of normal quartic fields, Ann. of Math. (2) 31 (1930), no. 3, 381–418. MR 1502952, DOI 10.2307/1968234
- A. Adrian Albert, A determination of the integers of all cubic fields, Ann. of Math. (2) 31 (1930), no. 4, 550–566. MR 1502961, DOI 10.2307/1968153
- A. Adrian Albert, A construction of all non-commutative rational division algebras of order eight, Ann. of Math. (2) 31 (1930), no. 4, 567–576. MR 1502962, DOI 10.2307/1968154 27. Abraham Adrian Albert, Normal division algebras of order 22m, Proc. Nat. Acad. Sci. U.S.A. 17 (1931), 389-392. 28. Abraham Adrian Albert, The structure of pure Riemann matrices with noncommutative multiplication algebras, Palermo Rendiconti 55 (1931), 57-115.
- A. Adrian Albert, On direct products, cyclic division algebras, and pure Riemann matrices, Trans. Amer. Math. Soc. 33 (1931), no. 1, 219–234. MR 1501586, DOI 10.1090/S0002-9947-1931-1501586-7
- A. Adrian Albert, On normal division algebras of type $R$ in thirty-six units, Trans. Amer. Math. Soc. 33 (1931), no. 1, 235–243. MR 1501587, DOI 10.1090/S0002-9947-1931-1501587-9 31. Abraham Adrian Albert, On the Wedderburn norm condition for cyclic algebras, Bull. Amer. Math. Soc. 37 (1931), 301-312. 32. Abraham Adrian Albert, A note on cyclic algebras of order 16, Bull. Amer. Math. Soc. 37 (1931), 727-730.
- A. Adrian Albert, On direct products, Trans. Amer. Math. Soc. 33 (1931), no. 3, 690–711. MR 1501610, DOI 10.1090/S0002-9947-1931-1501610-1 34. Abraham Adrian Albert, Division algebras over an algebraic field, Bull. Amer. Math. Soc. 37 (1931), 777-784.
- A. Adrian Albert, The structure of matrices with any normal division algebra of multiplications, Ann. of Math. (2) 32 (1931), no. 1, 131–148. MR 1502987, DOI 10.2307/1968420
- A. Adrian Albert, On the Construction of Cyclic Algebras with a Given Exponent, Amer. J. Math. 54 (1932), no. 1, 1–13. MR 1506868, DOI 10.2307/2371072
- A. Adrian Albert, Algebras of degree $2^e$ and pure Riemann matrices, Ann. of Math. (2) 33 (1932), no. 2, 311–318. MR 1503054, DOI 10.2307/1968332 38. Abraham Adrian Albert, A construction of non-cyclic normal division algebras, Bull. Amer. Math. Soc. 38 (1932), 449-456.
- A. Adrian Albert, Normal division algebras of degree four over an algebraic field, Trans. Amer. Math. Soc. 34 (1932), no. 2, 363–372. MR 1501642, DOI 10.1090/S0002-9947-1932-1501642-4
- A. Adrian Albert, On normal simple algebras, Trans. Amer. Math. Soc. 34 (1932), no. 3, 620–625. MR 1501653, DOI 10.1090/S0002-9947-1932-1501653-9 41. Abraham Adrian Albert, A note on division algebras of order sixteen, Bull. Amer. Math. Soc. 38 (1932), 703-706.
- A. Adrian Albert and Helmut Hasse, A determination of all normal division algebras over an algebraic number field, Trans. Amer. Math. Soc. 34 (1932), no. 3, 722–726. MR 1501659, DOI 10.1090/S0002-9947-1932-1501659-X 43. Abraham Adrian Albert, A note on the equivalence of algebras of degree two, Bull. Amer. Math. Soc. 39 (1933), 257-258. 44. Abraham Adrian Albert, On primary normal division algebras of degree eight, Bull. Amer. Math. Soc. 39 (1933), 265-272.
- A. Adrian Albert, Non-cyclic algebras of degree and exponent four, Trans. Amer. Math. Soc. 35 (1933), no. 1, 112–121. MR 1501674, DOI 10.1090/S0002-9947-1933-1501674-7
- A. Adrian Albert, The Integers Represented by Sets of Ternary Quadratic Forms, Amer. J. Math. 55 (1933), no. 1-4, 274–292. MR 1506964, DOI 10.2307/2371130
- A. Adrian Albert, On universal sets of positive ternary quadratic forms, Ann. of Math. (2) 34 (1933), no. 4, 875–878. MR 1503139, DOI 10.2307/1968705 48. Abraham Adrian Albert, A note on the Dickson theorem on universal ternaries, Bull. Amer. Math. Soc. 39 (1933), 585-588. 49. Abraham Adrian Albert, Normal division algebras over algebraic number fields not of finite degree, Bull. Amer. Math. Soc. 39 (1933), 746-749.
- A. Adrian Albert, Cyclic fields of degree eight, Trans. Amer. Math. Soc. 35 (1933), no. 4, 949–964. MR 1501727, DOI 10.1090/S0002-9947-1933-1501727-3
- A. Adrian Albert, On the construction of Riemann matrices. I, Ann. of Math. (2) 35 (1934), no. 1, 1–28. MR 1503140, DOI 10.2307/1968116
- A. Adrian Albert, On a certain algebra of quantum mechanics, Ann. of Math. (2) 35 (1934), no. 1, 65–73. MR 1503142, DOI 10.2307/1968118 53. Abraham Adrian Albert, Normal division algebras of degree 4 over F of characteristic 2, Amer. J. Math. 56 (1934), 75-86. 54. Abraham Adrian Albert, Integral domains of rational generalized quaternion algebras, Bull. Amer. Soc. 40 (1934), 164-176.
- A. Adrian Albert, On certain imprimitive fields of degree $p^2$ over $P$ of characteristic $p$, Ann. of Math. (2) 35 (1934), no. 2, 211–219. MR 1503156, DOI 10.2307/1968426
- A. Adrian Albert, Normal division algebras over a modular field, Trans. Amer. Math. Soc. 36 (1934), no. 2, 388–394. MR 1501750, DOI 10.1090/S0002-9947-1934-1501750-X
- A. Adrian Albert, A solution of the principal problem in the theory of Riemann matrices, Ann. of Math. (2) 35 (1934), no. 3, 500–515. MR 1503176, DOI 10.2307/1968747 58. Abraham Adrian Albert, Cyclic fields of degree p, Bull. Amer. Math. Soc. 40 (1934), 625-631.
- A. Adrian Albert, On normal Kummer fields over a non-modular field, Trans. Amer. Math. Soc. 36 (1934), no. 4, 885–892. MR 1501774, DOI 10.1090/S0002-9947-1934-1501774-2 60. Abraham Adrian Albert, Involutorial simple algebras and real Riemann matrices, Proc. Nat. Acad. Sci. U.S.A. 20 (1934), 676-681. 61. Abraham Adrian Albert, The principal matrices of a Riemann matrix, Bull. Amer. Math. Soc. 40 (1934), 843-846.
- A. Adrian Albert, A note on the Poincaré theorem on impure Riemann matrices, Ann. of Math. (2) 36 (1935), no. 1, 151–156. MR 1503214, DOI 10.2307/1968670
- A. Adrian Albert, On the construction of Riemann matrices. II, Ann. of Math. (2) 36 (1935), no. 2, 376–394. MR 1503230, DOI 10.2307/1968578
- A. Adrian Albert, On cyclic fields, Trans. Amer. Math. Soc. 37 (1935), no. 3, 454–462. MR 1501797, DOI 10.1090/S0002-9947-1935-1501797-4
- A. Adrian Albert, Involutorial simple algebras and real Riemann matrices, Ann. of Math. (2) 36 (1935), no. 4, 886–964. MR 1503260, DOI 10.2307/1968595
- A. Adrian Albert, Normal division algebras of degree $p^e$ over $F$ of characteristic $p$, Trans. Amer. Math. Soc. 39 (1936), no. 1, 183–188. MR 1501840, DOI 10.1090/S0002-9947-1936-1501840-3
- A. Adrian Albert, Simple algebras of degree $p^e$ over a centrum of characteristic $p$, Trans. Amer. Math. Soc. 40 (1936), no. 1, 112–126. MR 1501866, DOI 10.1090/S0002-9947-1936-1501866-X
- Irving Kaplansky, Abraham Adrian Albert. November 9, 1905–June 6, 1972, A century of mathematics in America, Part I, Hist. Math., vol. 1, Amer. Math. Soc., Providence, RI, 1988, pp. 244–264. MR 1003173, DOI 10.1215/ijm/1258488156 69. Abraham Adrian Albert, p-algebras over a field generated by one indeterminate, Bull. Amer. Math. Soc. 43 (1937), 733-736.
- A. Adrian Albert, Normalized integral bases of algebraic number fields. I, Ann. of Math. (2) 38 (1937), no. 4, 923–957. MR 1503382, DOI 10.2307/1968847 71. Abraham Adrian Albert, A quadratic form problem in the calculus of variations, Bull. Amer. Math. Soc. 44 (1938), 250-253. 72. Abraham Adrian Albert, Non-cyclic algebras with pure maximal subfields, Bull. Amer. Math Soc. 44 (1938), 576-579.
- A. Adrian Albert, Symmetric and alternate matrices in an arbitrary field. I, Trans. Amer. Math. Soc. 43 (1938), no. 3, 386–436. MR 1501952, DOI 10.1090/S0002-9947-1938-1501952-6
- A. Adrian Albert, Quadratic null forms over a function field, Ann. of Math. (2) 39 (1938), no. 2, 494–505. MR 1503420, DOI 10.2307/1968799
- A. Adrian Albert, On cyclic algebras, Ann. of Math. (2) 39 (1938), no. 3, 669–682. MR 1503431, DOI 10.2307/1968641 76. Abraham Adrian Albert, A note on normal division algebras of prime degree, Bull. Amer. Math. Soc. 44 (1938), 649-652.
- A. A. Albert, On ordered algebras, Bull. Amer. Math. Soc. 46 (1940), 521–522. MR 1972, DOI 10.1090/S0002-9904-1940-07252-0
- A. A. Albert, On $p$-adic fields and rational division algebras, Ann. of Math. (2) 41 (1940), 674–693. MR 2861, DOI 10.2307/1968740
- A. A. Albert, A rule for computing the inverse of a matrix, Amer. Math. Monthly 48 (1941), 198–199. MR 3603, DOI 10.2307/2304250
- A. A. Albert, Division algebras over a function field, Duke Math. J. 8 (1941), 750–762. MR 6168
- A. A. Albert, Quadratic forms permitting composition, Ann. of Math. (2) 43 (1942), 161–177. MR 6140, DOI 10.2307/1968887
- A. A. Albert, Non-associative algebras. I. Fundamental concepts and isotopy, Ann. of Math. (2) 43 (1942), 685–707. MR 7747, DOI 10.2307/1968960
- A. A. Albert, Non-associative algebras. II. New simple algebras, Ann. of Math. (2) 43 (1942), 708–723. MR 7748, DOI 10.2307/1968961
- A. A. Albert, The radical of a non-associative algebra, Bull. Amer. Math. Soc. 48 (1942), 891–897. MR 7396, DOI 10.1090/S0002-9904-1942-07814-1
- A. A. Albert, An inductive proof of Descartes’ rule of signs, Amer. Math. Monthly 50 (1943), 178–180. MR 7806, DOI 10.2307/2302399
- A. A. Albert, Discussions and Notes: A Suggestion for a Simplified Trigonometry, Amer. Math. Monthly 50 (1943), no. 4, 251–253. MR 1525668, DOI 10.2307/2303930
- A. A. Albert, Quasigroups. I, Trans. Amer. Math. Soc. 54 (1943), 507–519. MR 9962, DOI 10.1090/S0002-9947-1943-0009962-7
- A. A. Albert, Algebras derived by non-associative matrix multiplication, Amer. J. Math. 66 (1944), 30–40. MR 9949, DOI 10.2307/2371893
- A. A. Albert, The matrices of factor analysis, Proc. Nat. Acad. Sci. U.S.A. 30 (1944), 90–95. MR 9829, DOI 10.1073/pnas.30.4.90
- A. A. Albert, The minimum rank of a correlation matrix, Proc. Nat. Acad. Sci. U.S.A. 30 (1944), 144–146. MR 10351, DOI 10.1073/pnas.30.6.144
- A. A. Albert, Quasigroups. II, Trans. Amer. Math. Soc. 55 (1944), 401–419. MR 10597, DOI 10.1090/S0002-9947-1944-0010597-1
- A. A. Albert, Two element generation of a separable algebra, Bull. Amer. Math. Soc. 50 (1944), 786–788. MR 11080, DOI 10.1090/S0002-9904-1944-08238-4 93. Abraham Adrian Albert, Quasiquaternion algebras, Ann. of Math. (2) 45 (1944), 623-638. MR 6, 115.
- A. A. Albert, On Jordan algebras of linear transformations, Trans. Amer. Math. Soc. 59 (1946), 524–555. MR 16759, DOI 10.1090/S0002-9947-1946-0016759-3
- A. A. Albert, The Wedderburn principal theorem for Jordan algebras, Ann. of Math. (2) 48 (1947), 1–7. MR 19601, DOI 10.2307/1969210
- A. A. Albert, Absolute valued real algebras, Ann. of Math. (2) 48 (1947), 495–501. MR 20550, DOI 10.2307/1969182
- A. A. Albert, A structure theory for Jordan algebras, Ann. of Math. (2) 48 (1947), 546–567. MR 21546, DOI 10.2307/1969128
- A. A. Albert, On the power-associativity of rings, Summa Brasil. Math. 2 (1948), no. 2, 21–32. MR 26044
- A. A. Albert, Power-associative rings, Trans. Amer. Math. Soc. 64 (1948), 552–593. MR 27750, DOI 10.1090/S0002-9947-1948-0027750-7
- A. A. Albert, On the right alternative algebras, Ann. of Math. (2) 50 (1949), 318–328. MR 28828, DOI 10.2307/1969457
- A. A. Albert, Absolute-valued algebraic algebras, Bull. Amer. Math. Soc. 55 (1949), 763–768. MR 30941, DOI 10.1090/S0002-9904-1949-09278-9
- A. A. Albert, A theory of trace-admissible algebras, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 317–322. MR 30511, DOI 10.1073/pnas.35.6.317
- A. A. Albert, Almost alternative algebras, Portugal. Math. 8 (1949), 23–36. MR 32609
- A. A. Albert, A note on the exceptional Jordan algebra, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 372–374. MR 35753, DOI 10.1073/pnas.36.7.372
- A. A. Albert, A theory of power-associative commutative algebras, Trans. Amer. Math. Soc. 69 (1950), 503–527. MR 38959, DOI 10.1090/S0002-9947-1950-0038959-X
- A. A. Albert, New simple power-associative algebras, Summa Brasil. Math. 2 (1951), 183–194. MR 48421
- A. A. Albert, Power-associative algebras, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, Amer. Math. Soc., Providence, R.I., 1952, pp. 25–32. MR 0045103
- A. A. Albert, On nonassociative division algebras, Trans. Amer. Math. Soc. 72 (1952), 296–309. MR 47027, DOI 10.1090/S0002-9947-1952-0047027-4
- A. A. Albert, On simple alternative rings, Canad. J. Math. 4 (1952), 129–135. MR 48420, DOI 10.4153/cjm-1952-013-x
- A. A. Albert, On commutative power-associative algebras of degree two, Trans. Amer. Math. Soc. 74 (1953), 323–343. MR 52409, DOI 10.1090/S0002-9947-1953-0052409-1
- A. A. Albert, Rational normal matrices satisfying the incidence equation, Proc. Amer. Math. Soc. 4 (1953), 554–559. MR 56570, DOI 10.1090/S0002-9939-1953-0056570-X
- A. A. Albert, The structure of right alternative algebras, Ann. of Math. (2) 59 (1954), 408–417. MR 61096, DOI 10.2307/1969709
- A. A. Albert and M. S. Frank, Simple Lie algebras of characteristic $p$, Univ. e Politec. Torino Rend. Sem. Mat. 14 (1954/55), 117–139. MR 79222
- A. A. Albert, Leonard Eugene Dickson, 1874–1954, Bull. Amer. Math. Soc. 61 (1955), 331–345. MR 70564, DOI 10.1090/S0002-9904-1955-09937-3
- A. A. Albert, On involutorial algebras, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 480–482. MR 70623, DOI 10.1073/pnas.41.7.480
- A. A. Albert, On Hermitian operators over the Cayley algebra, Proc. Nat. Acad. Sci. U.S.A. 41 (1955), 639–640. MR 71416, DOI 10.1073/pnas.41.9.639
- A. A. Albert, A property of special Jordan algebras, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 624–625. MR 81271, DOI 10.1073/pnas.42.9.624
- A. A. Albert, The norm form of a rational division algebra, Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 506–509. MR 86807, DOI 10.1073/pnas.43.6.506
- A. A. Albert, On certain trinomial equations in finite fields, Ann. of Math. (2) 66 (1957), 170–178. MR 87691, DOI 10.2307/1970123 120. Abraham Adrian Albert, (with B. Muckenhoupt), On matrices of trace zero, Michigan Math. J. 4 (1957), 1-3. MR 18, 786.
- A. A. Albert, On partially stable algebras, Trans. Amer. Math. Soc. 84 (1957), 430–443. MR 92778, DOI 10.1090/S0002-9947-1957-0092778-3
- A. A. Albert and N. Jacobson, On reduced exceptional simple Jordan algebras, Ann. of Math. (2) 66 (1957), 400–417. MR 88487, DOI 10.2307/1969898
- A. A. Albert, A property of ordered rings, Proc. Amer. Math. Soc. 8 (1957), 128–129. MR 82480, DOI 10.1090/S0002-9939-1957-0082480-1
- A. A. Albert and John Thompson, Two element generation of the projective unimodular group, Bull. Amer. Math. Soc. 64 (1958), 92–93. MR 96728, DOI 10.1090/S0002-9904-1958-10169-X
- A. A. Albert, Addendum to the paper on partially stable algebras, Trans. Amer. Math. Soc. 87 (1958), 57–62. MR 92779, DOI 10.1090/S0002-9947-1958-0092779-6
- A. A. Albert, A construction of exceptional Jordan division algebras, Ann. of Math. (2) 67 (1958), 1–28. MR 91946, DOI 10.2307/1969922
- A. A. Albert, On the orthogonal equivalence of sets of real symmetric matrices, J. Math. Mech. 7 (1958), 219–235. MR 0092753, DOI 10.1512/iumj.1958.7.57018
- A. A. Albert, A solvable exceptional Jordan algebra, J. Math. Mech. 8 (1959), 331–337. MR 0101875, DOI 10.1512/iumj.1959.8.58022
- A. A. Albert and L. J. Paige, On a homomorphism property of certain Jordan algebras, Trans. Amer. Math. Soc. 93 (1959), 20–29. MR 108524, DOI 10.1090/S0002-9947-1959-0108524-2
- A. A. Albert and John Thompson, Two-element generation of the projective unimodular group, Illinois J. Math. 3 (1959), 421–439. MR 106951
- A. A. Albert, Finite noncommutative division algebras, Proc. Amer. Math. Soc. 9 (1958), 928–932. MR 103212, DOI 10.1090/S0002-9939-1958-0103212-5
- A. A. Albert, Finite division algebras and finite planes, Proc. Sympos. Appl. Math., Vol. 10, American Mathematical Society, Providence, R.I., 1960, pp. 53–70. MR 0116036
- A. A. Albert, On the collineation groups associated with twisted fields, Calcutta Math. Soc. Golden Jubilee Commemoration Vol. (1958/59), Part II, Calcutta Math. Soc., Calcutta, 1958/1959, pp. 485–497. MR 0159854
- A. A. Albert, On the collineation groups of certain non-desarguesian planes, Portugal. Math. 18 (1959), 207–224. MR 130613
- A. A. Albert, Generalized twisted fields, Pacific J. Math. 11 (1961), 1–8. MR 122850
- A. A. Albert, Isotopy for generalized twisted fields, An. Acad. Brasil. Ci. 33 (1961), 265–275. MR 139639
- A. A. Albert, On involutorial associative division algebras, Scripta Math. 26 (1963), 309–316 (1963). MR 179202
- A. A. Albert, On the nuclei of a simple Jordan algebra, Proc. Nat. Acad. Sci. U.S.A. 50 (1963), 446–447. MR 153718, DOI 10.1073/pnas.50.3.446 139. Abraham Adrian Albert, Finite planes for the high school, The Math. Teacher 55 (1962), 165-169.
- A. A. Albert, A normal form for Reimann matrices, Canadian J. Math. 17 (1965), 1025–1029. MR 182628, DOI 10.4153/CJM-1965-097-0
- A. A. Albert, On exceptional Jordan division algebras, Pacific J. Math. 15 (1965), 377–404. MR 182647
- A. A. Albert, On associative division algebras of prime degree, Proc. Amer. Math. Soc. 16 (1965), 799–802. MR 179203, DOI 10.1090/S0002-9939-1965-0179203-9
- A. A. Albert, The finite planes of Ostrom, Bol. Soc. Mat. Mexicana (2) 11 (1966), 1–13. MR 231271
- A. A. Albert, New results on associative division algebras, J. Algebra 5 (1967), 110–132. MR 202757, DOI 10.1016/0021-8693(67)90030-0
- A. A. Albert, On some properties of biabelian fields, An. Acad. Brasil. Ci. 38 (1966), 217–221. MR 207683
- A. A. Albert, On certain polynomial systems, Scripta Math. 28 (1967), 15–19 (1967). MR 211990
- A. A. Albert, On associative division algebras, Bull. Amer. Math. Soc. 74 (1968), 438–454. MR 222114, DOI 10.1090/S0002-9904-1968-11963-9
- A. A. Albert, A note on certain cyclic algebras, J. Algebra 14 (1970), 70–72. MR 251066, DOI 10.1016/0021-8693(70)90133-X
- A. A. Albert, Tensor products of quaternion algebras, Proc. Amer. Math. Soc. 35 (1972), 65–66. MR 297803, DOI 10.1090/S0002-9939-1972-0297803-6
- S. A. Amitsur, On central division algebras, Israel J. Math. 12 (1972), 408–420. MR 318216, DOI 10.1007/BF02764632
- Richard Block, New simple Lie algebras of prime characteristic, trans. Amer. Math. Soc. 89 (1958), 421–449. MR 0100010, DOI 10.1090/S0002-9947-1958-0100010-8
- Richard Brauer, Über Systeme hyperkomplexer Zahlen, Math. Z. 30 (1929), no. 1, 79–107 (German). MR 1545045, DOI 10.1007/BF01187754
- Richard Brauer, Untersuchungen über die arithmetischen Eigenschaften von Gruppen linearer Substitutionen, Math. Z. 31 (1930), no. 1, 733–747 (German). MR 1545145, DOI 10.1007/BF01246444 154. R. Brauer, On normal division algebras of index five, Proc. Nat. Acad. Sci. U.S.A. 24 (1938), 243-246. 155. R. Brauer, H. Hasse and E. Noether, Beweis eines Hauptsatzes in der Theorie der Algebren, J. Reine Angew. Math. 167 (1931), 399-404. 156. F. Cecioni, Sopra un tipo di algebre prive di divisore dello zero, Rend. Circ. Mat. Palermo 47 (1923), 209-254.
- P. M. Cohn, On homomorphic images of special Jordan algebras, Canad. J. Math. 6 (1954), 253–264. MR 60496, DOI 10.4153/cjm-1954-026-9
- L. E. Dickson, New division algebras, Trans. Amer. Math. Soc. 28 (1926), no. 2, 207–234. MR 1501341, DOI 10.1090/S0002-9947-1926-1501341-6
- L. E. Dickson, Construction of division algebras, Trans. Amer. Math. Soc. 32 (1930), no. 2, 319–334. MR 1501540, DOI 10.1090/S0002-9947-1930-1501540-4
- Marguerite Straus Frank, A new class of simple Lie algebras, Proc. Nat. Acad. Sci. U.S.A. 40 (1954), 713–719. MR 66360, DOI 10.1073/pnas.40.8.713
- Helmut Hasse, Zum Existenzsatz von Grunwald in der Klassenkörpertheorie, J. Reine Angew. Math. 188 (1950), 40–64 (German). MR 40340, DOI 10.1515/crll.1950.188.40
- G. Hochschild, Semi-simple algebras and generalized derivations, Amer. J. Math. 64 (1942), 677–694. MR 7009, DOI 10.2307/2371713
- F. D. Jacobson and N. Jacobson, Classification and representation of semi-simple Jordan algebras, Trans. Amer. Math. Soc. 65 (1949), 141–169. MR 29367, DOI 10.1090/S0002-9947-1949-0029367-8
- N. Jacobson, A note on non-associative algebras, Duke Math. J. 3 (1937), no. 3, 544–548. MR 1546009, DOI 10.1215/S0012-7094-37-00343-0
- N. Jacobson, A theorem on the structure of Jordan algebras, Proc. Nat. Acad. Sci. U.S.A. 42 (1956), 140–147. MR 75934, DOI 10.1073/pnas.42.3.140
- Nathan Jacobson, Structure and representations of Jordan algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX, American Mathematical Society, Providence, R.I., 1968. MR 0251099 167. P. Jordan, Über eine Klasse nichtassoziativer hyperkomplexer Algebren, Nachr. Ges. Wiss. Göttingen 1932, 569-575.
- P. Jordan, J. von Neumann, and E. Wigner, On an algebraic generalization of the quantum mechanical formalism, Ann. of Math. (2) 35 (1934), no. 1, 29–64. MR 1503141, DOI 10.2307/1968117
- G. K. Kalisch, On special Jordan algebras, Trans. Amer. Math. Soc. 61 (1947), 482–494. MR 20551, DOI 10.1090/S0002-9947-1947-0020551-4
- Erwin Kleinfeld, Simple alternative rings, Ann. of Math. (2) 58 (1953), 544–547. MR 58581, DOI 10.2307/1969753
- Erwin Kleinfeld, Alternative nil rings, Ann. of Math. (2) 66 (1957), 395–399. MR 87638, DOI 10.2307/1969897
- A. I. Kostrikin and I. R. Šafarevič, Graded Lie algebras of finite characteristic, Izv. Akad. Nauk SSSR Ser. Mat. 33 (1969), 251–322 (Russian). MR 0252460
- Kevin McCrimmon, Finite power-associative division rings, Proc. Amer. Math. Soc. 17 (1966), 1173–1177. MR 204479, DOI 10.1090/S0002-9939-1966-0204479-X
- Kevin McCrimmon, A note on finite division rings, Proc. Amer. Math. Soc. 23 (1969), 598–600. MR 254110, DOI 10.1090/S0002-9939-1969-0254110-5
- M. L. Racine, A note on quadratic Jordan algebras of degree $3$, Trans. Amer. Math. Soc. 164 (1972), 93–103. MR 304447, DOI 10.1090/S0002-9947-1972-0304447-0 176. C. Rosati, Sulle matrici di Riemann, Rend. Circ. Mat. Palermo 53 (1929), 79-134. 177. K. Soda, Einige Sätze über Matrizen, Japan J. Math. 13 (1936), 361-365.
- C. L. Siegel, Lectures on Riemann matrices, Tata Institute of Fundamental Research Lectures on Mathematics, No. 28, Tata Institute of Fundamental Research, Bombay, 1963. Notes by S. Raghavan and S. S. Rangachari. MR 0266959
- T. A. Springer, The classification of reduced exceptional simple Jordan algebras, Nederl. Akad. Wetensch. Proc. Ser.A 63 = Indag. Math. 22 (1960), 414–422. MR 0147520 180. O. Teichmüller, Multiplikation zyklischer Normalringen, Deutsch. Math. 1936, 197-238. 181. O. Teichmüller, p-Algebren, Deutsch. Math. 1936, 362-388.
- Shianghaw Wang, A counter-example to Grunwald’s theorem, Ann. of Math. (2) 49 (1948), 1008–1009. MR 26992, DOI 10.2307/1969410
- Shianghaw Wang, On Grunwald’s theorem, Ann. of Math. (2) 51 (1950), 471–484. MR 33801, DOI 10.2307/1969335
- J. H. M. Wedderburn, A type of primitive algebra, Trans. Amer. Math. Soc. 15 (1914), no. 2, 162–166. MR 1500970, DOI 10.1090/S0002-9947-1914-1500970-5
- J. H. M. Wedderburn, On division algebras, Trans. Amer. Math. Soc. 22 (1921), no. 2, 129–135. MR 1501164, DOI 10.1090/S0002-9947-1921-1501164-3
- Hermann Weyl, On generalized Riemann matrices, Ann. of Math. (2) 35 (1934), no. 4, 714–729. MR 1503189, DOI 10.2307/1968487
- Hermann Weyl, Generalized Riemann matrices and factor sets, Ann. of Math. (2) 37 (1936), no. 3, 709–745. MR 1503306, DOI 10.2307/1968485
- D. Zelinsky, A. A. Albert, Amer. Math. Monthly 80 (1973), 661–665. MR 313017, DOI 10.2307/2319167
Additional Information
- Journal: Bull. Amer. Math. Soc. 80 (1974), 1075-1100
- DOI: https://doi.org/10.1090/S0002-9904-1974-13622-0
- MathSciNet review: 0342341