Available in electronic format
Available in print format		 Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues: 1891 - Present
Previous Article | Next Article
     

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): Alexei Kanel-Belov and Louis Halle Rowen
Title: Computational aspects of polynomial identities
Additional book information: Research Notes in Mathematics, vol. 9, A~K Peters, Ltd., Wellesley, MA, 2005, xxi + 378, US$69.00, 1-56881-163-2

References:

[1]
S. A. Amitsur, The T-ideals of the free ring, J. London Math. Soc. 30 (1955), 470-475. MR 0071408 (17:122c)

[2]
S. A. Amitsur and J. Levitzki, Minimal identities for algebras, Proc. Amer. Math. Soc. 1 (1950), 449-463. MR 0036751 (12:155d).

[3]
A. Z. Anan'in, The representability of finitely generated algebras with chain condition, Arch. Math. 59 (1992), 1-5. MR 1166010 (93g:16036)

[4]
A. Ya. Belov, On non-Specht varieties, Fundam. Prikl. Mat. 5 (1999), 47-66 (Russian). MR 1799544 (2001k:16040)

[5]
A. Braun, The nilpotency of the radical in a finitely generated PI-ring, J. Algebra 89 (1984), 375-396. MR 0751151 (85m:16007)

[6]
M. Dehn, Über die Grundlagen der projectiven Geometrie und allgemeine Zahlsysteme, Math. Ann. 85 (1922), 184-193.

[7]
V. Drensky and E. Formanek, Polynomial Identity Rings, Birkhäuser, 2004. MR 2064082 (2005c:16040)

[8]
E. Formanek, Central polynomials for matrix rings, J. Algebra 23 (1972), 129-132. MR 0302689 (46:1833)

[9]
A. Giambruno and M. Zaicev, Exponential codimension growth of PI algebras: an exact estimate, Adv. Math. 142 (1999), 221-243. MR 1680198 (2000a:16048)

[10]
A. Giambruno and M. Zaicev, Polynomial Identities and Asymptotic Methods, Amer. Math. Soc., 2005.

[11]
A. V. Grishin, A variety of associative rings is not Spechtian, Uspekhi Mat. Nauk 54 (1999), 157-158 (Russian). Translation: Russian Math. Surveys 54 (1999), 1025-1026. MR 1741669 (2000m:16035)

[12]
M. Hall, Projective planes, Trans. Amer. Math. Soc. 54 (1943), 229-277. MR 0008892 (5:72c)

[13]
I. Kaplansky, Rings with a polynomial identity, Bull. Amer. Math. Soc. 54 (1948), 575-580. MR 0025451 (10:7a)

[14]
A. R. Kemer, Capelli identities and nilpotency of the radical in finitely generated PI-algebras, Dokl. Akad. Nauk SSSR 255 (1980), 793-797 (Russian). Translation: Soviet Math. Dokl. 22 (1980). MR 0600746 (82c:16019)

[15]
A. R. Kemer, Solution of the problem as to whether associative algebras have a finite basis of identities, Dokl. Akad. Nauk SSSR 298 (1988), 273-277. MR 0937115 (89d:16023)

[16]
A. R. Kemer, Ideals of Identities of Associative Algebras, Amer. Math. Soc., 1991. MR 1108620 (92f:16031)

[17]
A. R. Kemer, The standard identity in characteristic $ p$: a conjecture of I. B. Volichenko, Israel J. Math. 81 (1993), 343-355. MR 1231198 (94f:16040)

[18]
B. Kostant, A theorem of Frobenius, a theorem of Amitsur-Levitski and cohomology theory, J. Math. Mech. 7 (1958), 237-264. MR 0092755 (19:1153e)

[19]
V. N. Latyshev, On Regev's theorem on identities in a tensor product of PI-algebras, Uspekhi Mat. Nauk 27 (1972), 213-214 (Russian). MR 0393114 (52:13924)

[20]
C. Procesi, The invariant theory of $ n\times n$ matrices, Adv. in Math. 19 (1976), 306-381. MR 0419491 (54:7512)

[21]
Y. P. Razmyslov, On a certain problem of Kaplansky, Izv. Akad. Nauk SSSR 37 (1973), 483-501 (Russian). Translation: Math. USSR-Izv. 7 (1973), 479-496. MR 0338063 (49:2830)

[22]
Y. P. Razmyslov, The Jacobson radical in PI-algebras, Alg. i Logika 13 (1974), 337-360 (Russian). Translation: Algebra and Logic 13 (1974), 192-204. MR 0419515 (54:7536)

[23]
Y. P. Razmyslov, Trace identities of full matrix algebras over a field of characteristic zero, Izv. Akad. Nauk SSSR 38 (1974), 723-756 (Russian). Translation: Math. USSR-Izv. 8 (1974), 727-760. MR 0506414 (58:22158)

[24]
A. Regev, Existence of identities in $ A \otimes B$, Israel J. Math. 11 (1972), 131-152. MR 0314893 (47:3442)

[25]
A. Regev, Asymptotics of codimensions of some P.I. algebras, pp. 159-172 in Trends in Ring Theory (Miskolc, 1996), V. Dlab and L. Márki, Editors, Canadian Math. Soc. Conference Proceedings Vol. 22, Amer. Math. Soc., 1998. MR 1491923 (98k:16033)

[26]
W. Schelter, Noncommutative affine PI rings are catenary, J. Algebra 51 (1978), 12-18. MR 0485980 (58:5772)

[27]
V. V. Shchigolev, Examples of infinitely based T-ideals, Fundam. Prikl. Mat 5 (1999), 307-321 (Russian). MR 1799533 (2001k:16044)

[28]
A. I. Shirshov, On some non-associative nil-rings and algebraic algebras, Mat. Sb. 41(83) (1957), 381-394 (Russian). MR 0089841 (19:727h)

[29]
A. I. Shirshov, On rings with identity relations, Math. Sb. 43(85) (1957), 277-283 (Russian). MR 0095192 (20:1698)

[30]
L. W. Small, Prime ideals in Noetherian PI-rings, Bull. Amer. Math. Soc. 79 (1973), 421-422. MR 0313307 (47:1862)

[31]
W. Specht, Gesetze in Ringen. I, Math. Z. 52 (1950), 557-589. MR 0035274 (11:711i)

[32]
W. Wagner, Über die Grundlagen der projektiven Geometrie und allgemeine Zahlststeme, Math. Z. 113 (1937), 528-567.

Additional Information:

Reviewer(s):
Edward Formanek
Affiliation: The Pennsylvania State University
Email: formanek@math.psu.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 43 (2006), 579-584.

MSC (2000): Primary 16R10
DOI: 10.1090/S0273-0979-06-01106-2
PII: S 0273-0979(06)01106-2
Posted: April 20, 2006
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google