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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]

S. A. Amitsur, An embedding of PI-rings, Proc. Amer. Math. Soc. 3 (1952), 3-9. MR 13:618b

[A2]

S. A. Amitsur, A general theory of radicals. I. Radicals in complete lattices, Amer. J. Math. 74 (1952), 774-786. MR 14:347e

[A3]

S. A. Amitsur, The identities of PI-rings, Proc. Amer. Math. Soc. 3 (1952), 27-34. MR 14:613b

[A4]

S. A. Amitsur, A general theory of radicals. II. Radicals in rings and bicategories, Amer. J. Math. 75 (1954), 100-125. MR 15:499b

[A5]

S. A. Amitsur, A general theory of radicals. III. Applications, Amer. J. Math. 75 (1954), 126-136. MR 15:499c

[A6]

S. A. Amitsur, Generic splitting fields of central simple algebras, Ann. of Math. 62 (1955), 8-43. MR 17:9d

[A7]

S. A. Amitsur, On rings with identities, J. London Math. Soc. 30 (1955), 464-470. MR 17:122b

[A8]

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

[A9]

S. A. Amitsur, Finite subgroups of division rings, Trans. Amer. Math. Soc. 80 (1955), 361-386. MR 17:577c

[A10]

S. A. Amitsur, Algebras over infinite fields, Proc. Amer. Math. Soc. 7 (1956), 35-48. MR 17:822b

[A11]

S. A. Amitsur, Radicals of polynomial rings, Canadian J. Math. 8 (1956), 355-361. MR 17:1179c

[A12]

S. A. Amitsur, A generalization of Hilbert's Nullstellensatz, Proc. Amer. Math. Soc. 8 (1957), 649-656. MR 19:384a

[A13]

S. A. Amitsur, Simple algebras and cohomology groups of arbitrary fields, Trans. Amer. Math. Soc. 10 (1959), 73-112. MR 21:78

[A14]

S. A. Amitsur, On the semi-simplicity of group algebras, Michigan J. Math. 6 (1959) 251-253. MR 0108540

[A15]

S. A. Amitsur, Groups with representations of bounded degree II, Illinois J. Math. 5 (1961), 198-205. MR 23:A225

[A16]

S. A. Amitsur, Homology groups and double complexes for arbitrary fields, J. Math. Soc. of Japan 14 (1962), 1-25. MR 26:2481

[A17]

S. A. Amitsur, Generalized polynomial identities and pivotal monomials, Trans. Amer. Math. Soc. 114 (1965), 210-226. MR 30:3117

[A18]

S. A. Amitsur, Rational identities and applications to algebra and geometry, J. Algebra 3 (1966), 304-359. MR 33:139

[A19]

S. A. Amitsur, Rings of quotients and Morita contexts, J. Algebra 17 (1971), 273-298. MR 54:2704

[A20]

S. A. Amitsur, 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]

S. A. Amitsur, On central division algebras, Israel J. Math. 12 (1972), 408-420. MR 47:6763

[A22]

S. A. Amitsur, Polynomial identities, Israel J. Math. 19 (1974), 183-199. MR 54:10326

[AL]

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

[AR]

S. A. Amitsur and A. Regev, PI-algebras and their cocharacters, J. Algebra 78 (1982), 248-254. MR 84b:16020

[Ar]

M. Artin, On Azumaya algebras and finite-dimensional representations of rings, J. Algebra 11 (1969), 532-563. MR 39:4217

[C]

P. M. Cohn, Free Rings and their Relations, second edition, London Math. Soc. Monograph No. 19, Academic Press, 1985. MR 87e:16006

[D]

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

[F]

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

[HP]

D. R. Hughes and F. C. Piper, Projective Planes, Springer-Verlag Graduate Texts in Math. No. 6, 1973. MR 48:12278

[IP]

I. M. Isaacs and D. S. Passman, Groups with representations of bounded degree, Canadian J. Math. 16 (1964), 299-309. MR 29:4811

[K]

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

[Ke1]

A. R. Kemer, 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]

A. R. Kemer, 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]

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

[P]

E. C. Posner, Prime rings satisfying a polynomial identity, Proc. Amer. Math. Soc. 11 (1960), 180-183. MR 22:2626

[Pr1]

C. Procesi, Non-commutative affine rings, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. 8 (1967), 239-255. MR 37:256

[Pr2]

C. Procesi, On a theorem of M. Artin, J. Algebra 22 (1972), 309-315. MR 46:1825

[Pr3]

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

[R1]

Y. P. Razmyslov, 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]

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 58:22158

[Re]

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

[S]

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

[W]

W. Wagner, 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