American Mathematical Society

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

MathSciNet review: 1567974
Full text of review: PDF This review is available free of charge.
Book Information:

Author: Jan R. Strooker
Title: Homological Questions in Local Algebra
Additional book information: Cambridge University Press, Cambridge 1990, 307 pp., US$34.50. ISBN 0-521-31526-3.

M. Auslander, Modules over unramified regular local rings, Illinois J. Math. 5 (1961), 631–647. MR 179211

Maurice Auslander and D. A. Buchsbaum, Unique factorization in regular local rings, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 733–734. MR 103906, DOI 10.1073/pnas.45.5.733

M. Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 23–58. MR 268188

David A. Buchsbaum and David Eisenbud, Algebra structures for finite free resolutions, and some structure theorems for ideals of codimension $3$, Amer. J. Math. 99 (1977), no. 3, 447–485. MR 453723, DOI 10.2307/2373926

E. Graham Evans and Phillip Griffith, The syzygy problem, Ann. of Math. (2) 114 (1981), no. 2, 323–333. MR 632842, DOI 10.2307/1971296

Melvin Hochster, Topics in the homological theory of modules over commutative rings, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 24, Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, Providence, R.I., 1975. Expository lectures from the CBMS Regional Conference held at the University of Nebraska, Lincoln, Neb., June 24–28, 1974. MR 0371879

Melvin Hochster, Canonical elements in local cohomology modules and the direct summand conjecture, J. Algebra 84 (1983), no. 2, 503–553. MR 723406, DOI 10.1016/0021-8693(83)90092-3

Melvin Hochster and Craig Huneke, Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), no. 1, 31–116. MR 1017784, DOI 10.1090/S0894-0347-1990-1017784-6

Melvin Hochster and Craig Huneke, Infinite integral extensions and big Cohen-Macaulay algebras, Ann. of Math. (2) 135 (1992), no. 1, 53–89. MR 1147957, DOI 10.2307/2946563

[K]

W. Krull, Primidealketten in allgemeinen Ringbereichen, Heidelberger Akad. Wiss. Math.-Natur. K1. 7 (1928), 7.

C. Peskine and L. Szpiro, Dimension projective finie et cohomologie locale. Applications à la démonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck, Inst. Hautes Études Sci. Publ. Math. 42 (1973), 47–119 (French). MR 374130

Christian Peskine and Lucien Szpiro, Syzygies et multiplicités, C. R. Acad. Sci. Paris Sér. A 278 (1974), 1421–1424 (French). MR 349659

Paul Roberts, Two applications of dualizing complexes over local rings, Ann. Sci. École Norm. Sup. (4) 9 (1976), no. 1, 103–106. MR 399075

Paul Roberts, Cohen-Macaulay complexes and an analytic proof of the new intersection conjecture, J. Algebra 66 (1980), no. 1, 220–225. MR 591254, DOI 10.1016/0021-8693(80)90121-0

Paul Roberts, Le théorème d’intersection, C. R. Acad. Sci. Paris Sér. I Math. 304 (1987), no. 7, 177–180 (French, with English summary). MR 880574

Jean-Pierre Serre, Algèbre locale. Multiplicités, Lecture Notes in Mathematics, vol. 11, Springer-Verlag, Berlin-New York, 1965 (French). Cours au Collège de France, 1957–1958, rédigé par Pierre Gabriel; Seconde édition, 1965. MR 0201468

Review Information:

Reviewer: Craig Huneke

Journal: Bull. Amer. Math. Soc. 26 (1992), 361-367
DOI: https://doi.org/10.1090/S0273-0979-1992-00280-X