|
Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Retrieve article in:
PDF DVI PostScript
Book Information
Author(s):
Vesselin Drensky and Edward Formanek
Title:
Polynomial identity rings
Additional book information:
Birkhäuser-Verlag,
2004,
viii+200,
US$39.95,
3-7643-7126-9
References:
-
- [Am1]
- Amitsur, S.A., A generalization of Hilbert's Nullstellensatz, Proc. Amer. Math. Soc. 8 (1957), 649-656. MR 0087644 (19:384a)
- [Am2]
- Amitsur, S.A., Rational identities and applications to algebra and geometry, J. Algebra 3 (1966), 304-359. MR 0191912 (33:139)
- [Am3]
- Amitsur, S.A., On central division algebras, Israel J. Math 12 (1972), 408-420. MR 0318216 (47:6763)
- [Am4]
- Amitsur, S.A., Polynomial identities, Israel J. Math 19 (1974), 183-199. MR 0422335 (54:10326)
- [Am5]
- Amitsur, S.A., Alternating identities, Proc. Ohio Univ. Conference on Ring Theor, Dekker (1974), 1-14. MR 0439877 (55:12758)
- [AmL]
- Amitsur, S.A. and Levitzki, J., Minimal identities for algebras, Proc. Amer. Math. Soc. 1 (1950), 449-463. MR 0036751 (12:155d)
- [AmP]
- Amitsur, S.A. and Procesi, C., Jacobson-rings and Hilbert algebras with polynomial identities, Ann. Mat. Pura Appl. 71 (1966), 61-72. MR 0206044 (34:5869)
- [Ar]
- Artin, M. On Azumaya algebras and finite dimensional representations of rings, J. Algebra 11 (1969), 532-563. MR 0242890 (39:4217)
- [ArS]
- Artin, M. and Schelter, W., Integral ring homomorphisms, Advances in Math. 39 (1981), 289-329. MR 0614165 (83e:16015)
- [Bel1]
- Belov, A., Counterexamples to the Specht problem, Sb. Math. 191 (3-4) (2000), 329-340. MR 1773251 (2001g:16043)
- [Bel2]
- Belov, A., Algebras with polynomial idenitities: Representations and combinatorial methods, Doctor of Science Dissertation, Moscow (2002).
- [Ber1]
- Berele, A., Trace identities and
graded invariants, Trans. Amer. Math. Soc. 309 (1988), 581-589. MR 0938917 (89m:17043) - [Bi]
- Birkhoff, G., On the structure of abstract algebras, Proc. Cambridge Phil. Soc. 31 (1935), 433-431.
- [Br]
- Braun, A., The nilpotency of the radical in a finitely generated PI-ring, J. Algebra 89 (1984), 375-396. MR 0751151 (85m:16007)
- [Bu]
- Burnside, W. On an unsettled question in the theory of discontinuous groups, Quart. J. Pure Appl. Math. 33 (1902), 230-238.
- [Ca]
- Cayley, A., A memoir on the theory of matrices, Philosophical Transactions of the Royal Society of London 141 (1858), 17-37.
- [De]
- Dehn, M., Uber die Grundlagen der projektiven Geometrie und allgemeine Zahlsysteme, Math. Ann. 85 (1922), 184-193.
- [Dr1]
- Drensky, V., Codimensions of
-ideals and Hilbert series of relatively free algebras, C.R. Acad. Bulgare Sci. 34 (1981), no. 9, 1201-1204. MR 0649144 (83g:16032) - [Dr2]
- Drensky, V., A minimal basis for identities of a second order matrix over a field of characteristic 0, Algebra and Logic 20 (1981), 282-290. MR 0648317 (83g:16031)
- [DuI]
- Dubnov, J. and Ivanov, J., Sur l'abaissement du degreé des polynômes en affineurs, C.R. Doklady. Acad. Sci. USSR 41 (1943), 96-98.
- [Fo1]
- Formanek, E., Central polynomials for matrix rings, J. Alg. 23 (1972), 129-132. MR 0302689 (46:1833)
- [Fo2]
- Formanek, E., Invariants and the ring of generic matrices, J. Algebra 89 (1984), no. 1, 178-223. MR 0748233 (85g:15031)
- [Fo3]
- Formanek, E., The Polynomial Identities and Invariants of
Matrices, CBMS Regional Conference Series in Mathematics, 78, AMS (1991). MR 1088481 (92d:16031) - [Fo4]
- Formanek, E., The ring of generic matrices, J. Algebra 258 (2002), no. 1, 310-320. MR 1958908 (2004a:16039)
- [GiZ]
- Giambruno, A. and Zaicev, M., Minimal varieties of algebras of exponential growth, Advances Math. 174 (2003), no. 2, 310-323. MR 1963697 (2004b:16028)
- [Ha]
- Hall, M., Projective planes, Trans. Amer. Math. Soc. 54 (1943), 229-277. MR 0008892 (5:72c)
- [He]
- Helling, H., Eine Kennzeichnung von Charakteren auf Gruppen und Assoziativen Algebren, Comm. in Alg. 1 (1974), 491-501. MR 0347880 (50:381)
- [Hi]
- Higman, Graham, On a conjecture of Nagata, Proc. Cam. Phil. Soc. 52 (1956), 1-4. MR 0073581 (17:453e)
- [Il]
- Iltyakov, A.V., Polynomial Identities of Finite Dimensional Lie Algebras, unpublished monograph (2003).
- [Ja]
- Jacobson, N., Structure theory for algebraic algebras of bounded degree, Ann. of Math. (1945), 695-707. MR 0014083 (7:238c)
- [Ka1]
- Kaplansky, I., Rings with a polynomial identity, Bull. Amer. Math. Soc. 54 (1948), 575-580. MR 0025451 (10:7a)
- [Ka2]
- Kaplansky, I., Topological representation of algebras. II, Trans. Amer. Math. Soc. 66 (1949), 464-491. MR 0032612 (11:317c)
- [Ka3]
- Kaplansky, I., ``Problems in the theory of rings" revisited, Amer. Math. Monthly 77 (1970), 445-454. MR 0258865 (41:3510)
- [Ke1]
- Kemer, A.R., Finite basability of identities of associative algebras (Russian), Algebra i Logika 26 (1987), 597-641; English translation: Algebra and Logic 26 (1987), 362-397. MR 0985840 (90b:08008)
- [Ke2]
- Kemer, A.R., The standard identity in characteristic
: a conjecture of I.B. Volichenko, Israel J. Math. 81 (1993), 343-355. MR 1231198 (94f:16040) - [Ke3]
- Kemer, A.R., Multilinear identities of the algebras over a field of characteristic
, Internat. J. Algebra Comput. 5 (1995), no. 2, 189-197. MR 1328550 (96d:16036) - [Ke4]
- Kemer, A.R., Remarks on the prime varieties, Israel J. Math. 96 (1996), part B, 341-356. MR 1433694 (98h:16034)
- [KrR]
- Krakowski, K. and Regev, A., The polynomial identities of the Grassman algebra, Trans. Amer. Math. Soc. 181 (1973), 429-438. MR 0325658 (48:4005)
- [Lev1]
- Levitzki, J., On a problem of Kurosch, Bull. Amer. Math. Soc. 52 (1946), 1033-1035. MR 0019600 (8:435a)
- [Lev2]
- Levitzki, J., A theorem on polynomial identities, Proc. Amer. Math. Soc. 1 (1950), 449-463. MR 0036751 (12:155d)
- [Mac]
- Macdonald, I. G., Symmetric functions and Hall polynomials, Second edition. With contributions by A. Zelevinsky. Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York (1995). MR 1354144 (96h:05207)
- [Mal]
- Mal'tsev, A.I., Unterschungen ays tem Gebiete des mathematicischen Logik, Mat. Sb. 1 43 (1936), 323-336.
- [Ne]
- Neumann, H., Varieties of Groups, Springer-Verlag, Berlin-New York (1967). MR 0215899 (35:6734)
- [OP]
- Oates, S., and Powell, M.B., Identical relations in finite gorups, J. Algebra 1 (1964), no. 1, 11-39. MR 0161904 (28:5108)
- [Pr]
- Procesi, C., The invariant theory of
matrices, Advances in Math. 19 (1976), 306-381. MR 0419491 (54:7512) - [Ra1]
- Razmyslov, Yu.P., On a problem of Kaplansky, Math USSR. Izv. 7 (1972), 479-496.
- [Ra2]
- Razmyslov, Yu.P., The Jacobson radical in PI-algebras, Algebra and Logic 13 (1974), no. 3, 192-204. MR 0419515 (54:7536)
- [Ra3]
- Razmyslov, Yu.P., Trace identities of full matrix algebras over a field of characteristic zero, Math. USSR Izv. 8 (1974), 724-760.
- [Ra4]
- Razmyslov, Yu.P., Existence of a finite basis for certain varieties of algebras, Algebra i Logika 13 (1974), 685-693; English translation: Algebra and Logic 13 (1974), 394-399. MR 0396686 (53:548)
- [RaZ]
- Razmyslov, Yu.P., and Zubrilin, K.A., Capelli identities and representations of finite type, Comm. Algebra 22 (1994), no. 14, 5733-5744. MR 1298747 (95h:17025)
- [Re1]
- Regev, A., The representations of
and explicit identities for P.I. algebras, J. Algebra 51 (1978), no. 1, 25-40. MR 0469965 (57:9745) - [Sch]
- Schelter, W., Noncommutative affine PI-algebras are catenary, J. Algebra 51 (1978), 12-18. MR 0485980 (58:5772)
- [Sh1]
- Shirshov, A.I., On some nonassociative nil-rings and algebraic algebras, Mat. Sb. 41 (1957), no. 3, 381-394.
- [Sh2]
- Shirshov, A.I., On rings with identity relations, Mat. Sb. 43 (1957), no. 2, 277-283. MR 0095192 (20:1698)
- [Sp]
- Specht, W., Gesetze in Ringen I, Math. Z. 52 (1950), 557-589. MR 0035274 (11:711i)
- [Va]
- Vaughan-Lee, M. The restricted Burnside problem, Second edition, London Mathematical Society Monographs, New Series, 8, The Clarendon Press, Oxford University Press, New York, 1993. MR 1364414 (98b:20047)
- [Wa]
- Wagner, W., Uber die Grundlagen der projektiven Geometrie und allgemeine Zahlsysteme, Math. Z. 113 (1937), 528-567. MR 1513106
- [Ze1]
- Zelmanov, Y., Solution of the restricted Burnside problem for groups of odd exponent (Russian), Izv. Akad. Nauk SSSR Ser. Mat. 54 (1990), no. 1, 42-59, 221; translation in Math. USSR-Izv. 36 (1991), no. 1, 41-60. MR 1044047 (91i:20037)
- [Ze2]
- Zelmanov, Y., Solution of the restricted Burnside problem for
-groups (Russian), Mat. Sb. 182 (1991), no. 4, 568-592; translation in Math. USSR-Sb. 72 (1992), no. 2, 543-565. MR 1119009 (93a:20063) - [Zu1]
- Zubrilin, K.A., Algebras satisfying Capelli identities, Sb. Math. 186 (1995), no. 3, 53-64. MR 1331808 (96c:16032)
- [Zu2]
- Zubrilin, K.A., On the largest nilpotent ideal in algebras satisfying Capelli identities, Sb. Math. 188 (1997), 1203-1211. MR 1481398 (98m:16027)
Additional Information:
Reviewer(s):
Louis
Rowen
Affiliation:
Bar-Ilan University
Email:
rowen@macs.biu.ac.il
Review Information:
Journal:
Bull. Amer. Math. Soc.
43
(2006),
259-267.
MSC
(2000):
Primary 16Rxx
DOI:
10.1090/S0273-0979-06-01082-2
PII:
S 0273-0979(06)01082-2
Posted:
February 16, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|