Some questions concerning alternative rings
HTML articles powered by AMS MathViewer
- by M. F. Smiley PDF
- Bull. Amer. Math. Soc. 57 (1951), 36-43
References
- 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, 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, Quasigroups. I, Trans. Amer. Math. Soc. 54 (1943), 507–519. MR 9962, DOI 10.1090/S0002-9947-1943-0009962-7
- 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, 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, Absolute valued real algebras, Ann. of Math. (2) 48 (1947), 495–501. MR 20550, DOI 10.2307/1969182
- 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, On the right alternative algebras, Ann. of Math. (2) 50 (1949), 318–328. MR 28828, DOI 10.2307/1969457 10. E. Artin, The influence of J. H. M. Wedderburn on the development of modern algebra, Bull. Amer. Math. Soc. vol. 56 (1950) pp. 65-72.
- Reinhold Baer, The homomorphism theorems for loops, Amer. J. Math. 67 (1945), 450–460. MR 12302, DOI 10.2307/2371960
- Richard Brauer, On a theorem of H. Cartan, Bull. Amer. Math. Soc. 55 (1949), 619–620. MR 29891, DOI 10.1090/S0002-9904-1949-09264-9
- Bailey Brown, An extension of the Jacobson radical, Proc. Amer. Math. Soc. 2 (1951), 114–117. MR 40286, DOI 10.1090/S0002-9939-1951-0040286-8
- Bailey Brown and Neal H. McCoy, Radicals and subdirect sums, Amer. J. Math. 69 (1947), 46–58. MR 19594, DOI 10.2307/2371653
- Bailey Brown and Neal H. McCoy, Some theorems on groups with applications to ring theory, Trans. Amer. Math. Soc. 69 (1950), 302–311. MR 38952, DOI 10.1090/S0002-9947-1950-0038952-7
- Richard H. Bruck, Some results in the theory of linear non-associative algebras, Trans. Amer. Math. Soc. 56 (1944), 141–199. MR 11083, DOI 10.1090/S0002-9947-1944-0011083-5
- R. H. Bruck, Contributions to the theory of loops, Trans. Amer. Math. Soc. 60 (1946), 245–354. MR 17288, DOI 10.1090/S0002-9947-1946-0017288-3
- Henri Cartan, Théorie de Galois pour les corps non commutatifs, Ann. Sci. École Norm. Sup. (3) 64 (1947), 59–77 (French). MR 0023237, DOI 10.24033/asens.942
- Roy Dubisch and Sam Perlis, The radical of an alternative algebra, Amer. J. Math. 70 (1948), 540–546. MR 25450, DOI 10.2307/2372198
- Alexandra Forsythe and Neal H. McCoy, On the commutativity of certain rings, Bull. Amer. Math. Soc. 52 (1946), 523–526. MR 16093, DOI 10.1090/S0002-9904-1946-08603-6
- G. N. Garrison, Quasi-groups, Ann. of Math. (2) 41 (1940), 474–487. MR 2150, DOI 10.2307/1968729
- Marshall Hall, Projective planes, Trans. Amer. Math. Soc. 54 (1943), 229–277. MR 8892, DOI 10.1090/S0002-9947-1943-0008892-4
- Marshall Hall Jr., Correction to “Projective planes.”, Trans. Amer. Math. Soc. 65 (1949), 473–474. MR 29515, DOI 10.1090/S0002-9947-1949-0029515-X
- Loo-Keng Hua, Some properties of a sfield, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 533–537. MR 31471, DOI 10.1073/pnas.35.9.533
- N. Jacobson, Cayley numbers and normal simple Lie algebras of type $\textrm {G}$, Duke Math. J. 5 (1939), 775–783. MR 598, DOI 10.1215/S0012-7094-39-00562-4
- N. Jacobson, Structure theory of simple rings without finiteness assumptions, Trans. Amer. Math. Soc. 57 (1945), 228–245. MR 11680, DOI 10.1090/S0002-9947-1945-0011680-8
- N. Jacobson, The radical and semi-simplicity for arbitrary rings, Amer. J. Math. 67 (1945), 300–320. MR 12271, DOI 10.2307/2371731 28. N. Jacobson and O. Taussky, Locally compact rings, Proc. Nat. Acad. Sci. U. S. A. vol. 21 (1931) pp. 106-108.
- Irving Kaplansky, Rings with a polynomial identity, Bull. Amer. Math. Soc. 54 (1948), 575–580. MR 25451, DOI 10.1090/S0002-9904-1948-09049-8
- Irving Kaplansky, Topological rings, Amer. J. Math. 69 (1947), 153–183. MR 19596, DOI 10.2307/2371662
- Irving Kaplansky, Topological rings, Bull. Amer. Math. Soc. 54 (1948), 809–826. MR 26643, DOI 10.1090/S0002-9904-1948-09058-9
- Neal H. McCoy, Subdirect sums of rings, Bull. Amer. Math. Soc. 53 (1947), 856–877. MR 21543, DOI 10.1090/S0002-9904-1947-08867-4
- Ruth Moufang, Zur Struktur der projektiven Geometrie der Ebene, Math. Ann. 105 (1931), no. 1, 536–601 (German). MR 1512725, DOI 10.1007/BF01455829
- Ruth Moufang, Die Einführung der idealen Elemente in die ebene Geometrie mit Hilfe des Satzes vom vollständigen Vierseit, Math. Ann. 105 (1931), no. 1, 759–778 (German). MR 1512741, DOI 10.1007/BF01455845
- Ruth Moufang, Die Schnittpunktsätze des projektiven speziellen Fünfecksnetzes in ihrer Abhängigkeit voneinander, Math. Ann. 106 (1932), no. 1, 755–795 (German). MR 1512782, DOI 10.1007/BF01455910 36. R. Moufang, Ein Satz über die Schnittpunktsätze des allgemeinen Fünfecksnetze [Das (A, B)-Netz], Math. Ann. vol. 107 (1932) pp. 124-139.
- Ruth Moufang, Die Desarguesschen Sätze vom Rang 10, Math. Ann. 108 (1933), no. 1, 296–310 (German). MR 1512850, DOI 10.1007/BF01452838 38. R. Moufang, Alternativkörper und der Satz vom vollständigen Vierseit (D, Abh. Math. Sem. Hamburgischen Univ. vol. 9 (1933) pp. 207-222.
- Ruth Moufang, Zur Struktur von Alternativkörpern, Math. Ann. 110 (1935), no. 1, 416–430 (German). MR 1512948, DOI 10.1007/BF01448037 40. K. Reidemeister, Grundlagen der Geometrie, Berlin, 1930.
- R. D. Schafer, Alternative algebras over an arbitrary field, Bull. Amer. Math. Soc. 49 (1943), 549–555. MR 8610, DOI 10.1090/S0002-9904-1943-07967-0
- R. D. Schafer, The Wedderburn principal theorem for alternative algebras, Bull. Amer. Math. Soc. 55 (1949), 604–614. MR 29895, DOI 10.1090/S0002-9904-1949-09259-5
- R. D. Schafer, Inner derivations of non-associative algebras, Bull. Amer. Math. Soc. 55 (1949), 769–776. MR 30944, DOI 10.1090/S0002-9904-1949-09281-9
- I. E. Segal, The group algebra of a locally compact group, Trans. Amer. Math. Soc. 61 (1947), 69–105. MR 19617, DOI 10.1090/S0002-9947-1947-0019617-4
- M. F. Smiley, An application of lattice theory to quasigroups, Bull. Amer. Math. Soc. 50 (1944), 782–786. MR 11312, DOI 10.1090/S0002-9904-1944-08237-2
- Malcolm F. Smiley, Alternative regular rings without nilpotent elements, Bull. Amer. Math. Soc. 53 (1947), 775–778. MR 22211, DOI 10.1090/S0002-9904-1947-08875-3
- M. F. Smiley, The radical of an alternative ring, Ann. of Math. (2) 49 (1948), 702–709. MR 25449, DOI 10.2307/1969053
- Malcolm F. Smiley, Application of a radical of Brown and McCoy to non-associative rings, Amer. J. Math. 72 (1950), 93–100. MR 32591, DOI 10.2307/2372136
- M. F. Smiley, A remark on a theorem of Marshall Hall, Proc. Amer. Math. Soc. 1 (1950), 342–343. MR 36225, DOI 10.1090/S0002-9939-1950-0036225-5 50. M. F. Smiley, Special alternative rings (abstract), Bull. Amer. Math. Soc. vol. 55 (1949) p. 1051. 51. H. Weyl, The classical groups, 2d ed., Princeton, 1946. 52. M. Zorn, Theorie der alternativen Ringe, Abh. Math. Sem. Hamburgischen Univ. vol. 8 (1930) pp. 123-147. 53. M. Zorn, Alternativkörper und quadratische Systeme, Abh. Math. Sem. Hamburgischen Univ. vol. 9 (1933) pp. 395-402. 54. M. Zorn, The automorphisms of Cayley’s non-associative algebra, Proc. Nat. Acad. Sci. U. S. A. vol. 21 (1935) pp. 355-358.
- Max Zorn, Alternative rings and related questions I: existence of the radical, Ann. of Math. (2) 42 (1941), 676–686. MR 5098, DOI 10.2307/1969256
Additional Information
- Journal: Bull. Amer. Math. Soc. 57 (1951), 36-43
- DOI: https://doi.org/10.1090/S0002-9904-1951-09437-9
- MathSciNet review: 0038950