American Mathematical Society

Book Review

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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.

[Au] M. Auslander, Modules over unramified regular local rings, Illinois J. Math. 5 (1961), 631–647. MR 0179211
[AB] Maurice Auslander and D. A. Buchsbaum, Unique factorization in regular local rings, Proc. Nat. Acad. Sci. U.S.A. 45 (1959), 733–734. MR 0103906
[Ar] M. Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 23–58. MR 0268188
[BE] 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 0453723, https://doi.org/10.2307/2373926
[EG] E. Graham Evans and Phillip Griffith, The syzygy problem, Ann. of Math. (2) 114 (1981), no. 2, 323–333. MR 632842, https://doi.org/10.2307/1971296
[Ho1] Melvin Hochster, Topics in the homological theory of modules over commutative rings, 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; Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 24. MR 0371879
[Ho2] Melvin Hochster, Canonical elements in local cohomology modules and the direct summand conjecture, J. Algebra 84 (1983), no. 2, 503–553. MR 723406, https://doi.org/10.1016/0021-8693(83)90092-3
[HH1] 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, https://doi.org/10.1090/S0894-0347-1990-1017784-6
[HH2] 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, https://doi.org/10.2307/2946563
[K] W. Krull, Primidealketten in allgemeinen Ringbereichen, Heidelberger Akad. Wiss. Math.-Natur. K1. 7 (1928), 7.
[PS1] 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 0374130
[PS2] Christian Peskine and Lucien Szpiro, Syzygies et multiplicités, C. R. Acad. Sci. Paris Sér. A 278 (1974), 1421–1424 (French). MR 0349659
[Ro1] Paul Roberts, Two applications of dualizing complexes over local rings, Ann. Sci. École Norm. Sup. (4) 9 (1976), no. 1, 103–106. MR 0399075
[Ro2] Paul Roberts, Cohen-Macaulay complexes and an analytic proof of the new intersection conjecture, J. Algebra 66 (1980), no. 1, 220–225. MR 591254, https://doi.org/10.1016/0021-8693(80)90121-0
[Ro3] 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
[Se] Jean-Pierre Serre, Algèbre locale. Multiplicités, Cours au Collège de France, 1957–1958, rédigé par Pierre Gabriel. Seconde édition, 1965. Lecture Notes in Mathematics, vol. 11, Springer-Verlag, Berlin-New York, 1965 (French). 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