Book Review

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Book Information:

Editors: Avinoam Mann, Amitai Regev, Louis Rowen, David J. Saltman and Lance W. Small (eds.)

Title: Selected papers of S. A. Amitsur with commentary

Additional book information: edited by Avinoam Mann, Amitai Regev, Louis Rowen, David J. Saltman and Lance W. Small (eds.), American Mathematical Society, Providence, RI, pt. 1, 2001, xx+583 pp., ISBN 0-8218-2924-6, $62.50$; pt. 2, xx+615 pp., ISBN 0-8218-2925-4, $63.50$; ISBN 0-8218-0688-2, $103.00$, Set

**[A1]**

*An embedding of PI-rings*, Proc. Amer. Math. Soc.

**3**(1952), 3-9. MR

**13:618b**

**[A2]**

*A general theory of radicals. I. Radicals in complete lattices*, Amer. J. Math.

**74**(1952), 774-786. MR

**14:347e**

**[A3]**

*The identities of PI-rings*, Proc. Amer. Math. Soc.

**3**(1952), 27-34. MR

**14:613b**

**[A4]**

*A general theory of radicals. II. Radicals in rings and bicategories*, Amer. J. Math.

**75**(1954), 100-125. MR

**15:499b**

**[A5]**

*A general theory of radicals. III. Applications*, Amer. J. Math.

**75**(1954), 126-136. MR

**15:499c**

**[A6]**

*Generic splitting fields of central simple algebras*, Ann. of Math.

**62**(1955), 8-43. MR

**17:9d**

**[A7]**

*On rings with identities*, J. London Math. Soc.

**30**(1955), 464-470. MR

**17:122b**

**[A8]**

*The T-ideals of the free ring*, J. London Math. Soc.

**30**(1955), 470-475. MR

**17:122c**

**[A9]**

*Finite subgroups of division rings*, Trans. Amer. Math. Soc.

**80**(1955), 361-386. MR

**17:577c**

**[A10]**

*Algebras over infinite fields*, Proc. Amer. Math. Soc.

**7**(1956), 35-48. MR

**17:822b**

**[A11]**

*Radicals of polynomial rings*, Canadian J. Math.

**8**(1956), 355-361. MR

**17:1179c**

**[A12]**

*A generalization of Hilbert's Nullstellensatz*, Proc. Amer. Math. Soc.

**8**(1957), 649-656. MR

**19:384a**

**[A13]**

*Simple algebras and cohomology groups of arbitrary fields*, Trans. Amer. Math. Soc.

**10**(1959), 73-112. MR

**21:78**

**[A14]**

*On the semi-simplicity of group algebras*, Michigan J. Math.

**6**(1959) 251-253. MR

**0108540**

**[A15]**

*Groups with representations of bounded degree II*, Illinois J. Math.

**5**(1961), 198-205. MR

**23:A225**

**[A16]**

*Homology groups and double complexes for arbitrary fields*, J. Math. Soc. of Japan

**14**(1962), 1-25. MR

**26:2481**

**[A17]**

*Generalized polynomial identities and pivotal monomials*, Trans. Amer. Math. Soc.

**114**(1965), 210-226. MR

**30:3117**

**[A18]**

*Rational identities and applications to algebra and geometry*, J. Algebra

**3**(1966), 304-359. MR

**33:139**

**[A19]**

*Rings of quotients and Morita contexts*, J. Algebra

**17**(1971), 273-298. MR

**54:2704**

**[A20]**

*Nil radicals. Historical notes and some new results*, Coll. Math. Soc. Janos Bolyai, vol. 6. Rings, modules and radicals (Keszthely, Hungary, 1971), 1973, pp. 47-65. MR

**50:374**

**[A21]**

*On central division algebras*, Israel J. Math.

**12**(1972), 408-420. MR

**47:6763**

**[A22]**

*Polynomial identities*, Israel J. Math.

**19**(1974), 183-199. MR

**54:10326**

**[AL]**

*Minimal identities for algebras*, Proc. Amer. Math. Soc.

**2**(1950), 449-463. MR

**12:155d**

**[AR]**

*PI-algebras and their cocharacters*, J. Algebra

**78**(1982), 248-254. MR

**84b:16020**

**[Ar]**

*On Azumaya algebras and finite-dimensional representations of rings*, J. Algebra

**11**(1969), 532-563. MR

**39:4217**

**[C]**

*Free Rings and their Relations*, second edition, London Math. Soc. Monograph No. 19, Academic Press, 1985. MR

**87e:16006**

**[D]**

*Über die Grundlagen der projektiven Geometrie und allgemeine Zahlsysteme*, Math. Ann.

**85**(1922), 184-193.

**[F]**

*Central polynomials for matrix rings*, J. Algebra

**23**(1972), 129-132. MR

**46:1833**

**[HP]**

*Projective Planes*, Springer-Verlag Graduate Texts in Math. No. 6, 1973. MR

**48:12278**

**[IP]**

*Groups with representations of bounded degree*, Canadian J. Math.

**16**(1964), 299-309. MR

**29:4811**

**[K]**

*Rings with a polynomial identity*, Bull. Amer. Math. Soc.

**54**(1948), 575-580. MR

**10:7a**

**[Ke1]**

*Finite basis property of identities of associative algebras*, Algebra i Logika

**26**(1987), 597-641 (Russian). Translation: Algebra and Logic

**26**(1988), 362-397. MR

**90b:08008**

**[Ke2]**

*Solution of the finite basis problem for identities of associative algebras*, Dokl. Akad. Nauk SSSR

**298**(1988), 273-277 (Russian). Translation: Soviet Math. Dokl.

**37**(1988), 60-64. MR

**89d:16023**

**[Ko]**

*A theorem of Frobenius, a theorem of Amitsur-Levitski, and cohomology theory*, J. Math. Mech.

**7**(1958), 237-264. MR

**19:1153e**

**[P]**

*Prime rings satisfying a polynomial identity*, Proc. Amer. Math. Soc.

**11**(1960), 180-183. MR

**22:2626**

**[Pr1]**

*Non-commutative affine rings*, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur.

**8**(1967), 239-255. MR

**37:256**

**[Pr2]**

*On a theorem of M. Artin*, J. Algebra

**22**(1972), 309-315. MR

**46:1825**

**[Pr3]**

*The invariant theory of matrices*, Adv. in Math.

**19**(1976), 306-381. MR

**54:7512**

**[R1]**

*On a problem of Kaplansky*, Izv. Akad. Nauk SSSR

**37**(1973), 483-501 (Russian). Translation: Math. USSR-Izv.

**7**(1973), 479-496. MR

**49:2830**

**[R2]**

*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

**58:22158**

**[Re]**

*Existence of identities in*, Israel J. Math.

**11**(1972), 131-152. MR

**47:3442**

**[S]**

*On rings with identity relations*, Math. Sb.

**43**(85) (1957), 277-283 (Russian). MR

**20:1698**

**[W]**

*Über die Grundlagen der projectiven Geometrie und allgemeine Zahlsysteme*, Math. Z.

**113**(1937), 528-567.

Review Information:

Reviewer: Edward Formanek

Affiliation: The Pennsylvania State University

Email: formanek@math.psu.edu

Journal: Bull. Amer. Math. Soc.

**40**(2003), 131-135

Published electronically: October 18, 2002

Review copyright: © Copyright 2002 American Mathematical Society