|
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
Book Information
Author(s):
Winfried Bruns and J\"urgen Herzog
Title:
Cohen-Macaulay rings
Additional book information:
Cambridge Studies in Advanced Mathematics, vol. 39, Cambridge University Press, Cambridge, 1993, xi + 403~pp., US$79.95. ISBN 0-521-41068-1
References:
- [AK]
- Altman, S. and S. Kleiman, Introduction to Grothendieck duality theory, Lecture Notes in Math., vol. 146, Springer-Verlag, Berlin, Heidelberg, and New York, 1970. MR 274461
- [Au]
- Auslander, M., Modules over unramified regular local rings, Illinois J. Math. 5 (1961), 631-645. MR 179211
- [B]
- Bass, H., On the ubiquity of Gorenstein rings, Math. Z. 82 (1963), 8--28. MR 153708
- [Bou]
- Boutot, J.-F., Singularités rationelles et quotients par les groupes réductifs, Invent. Math. 88 (1987), 65--68. MR 877006
- [C]
- Cohen, I.S., On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc. 59 (1946), 54-106. MR 16094
- [F1]
- Fulton, W., Algebraic curves, Benjamin, New York, 1969. MR 313252
- [F2]
- _____, Intersection theory, Springer-Verlag, Berlin, Heidelberg, and New York, 1984. MR 732620
- [Ha]
- Hartshorne, R., Algebraic geometry, Springer-Verlag, New York, Heidelberg, and Berlin, 1977. MR 463157
- [He]
- Heitmann, R., A counterexample to the rigidity conjecture for rings, Bull. Amer. Math. Soc. (N.S.) 29 (1993), 94--97. MR 1197425
- [Ho1]
- Hochster, M. , Topics in the homological theory of modules over commutative rings, CBMS Regional Conf. Ser. in Math., vol. 24, Amer. Math. Soc., Providence, RI, 1975. MR 371879
- [Ho2]
- _____, Canonical elements in local cohomology modules and the direct summand conjecture, J. Algebra 84 (1983), 503--553. MR 723406
- [HoE]
- Hochster, M., and J.A. Eagon, Cohen-Macaulay rings, invariant theory, and the generic perfection of determinantal loci, Amer. J. Math. 93 (1971), 1020--1058. MR 302643
- [HH1]
- Hochster, M., and J.A. Eagon, Tight closure, invariant theory, and the Briançon-Skoda theorem, J. Amer. Math. Soc. 3 (1990), 31--116. MR 1017784
- [HH2]
- Hochster, M., and J.A. Eagon, Infinite integral extensions and big Cohen-Macaulay algebras, Ann. of Math. 135 (1992), 53--89. MR 1147957
- [HH3]
- Hochster, M., and J.A. Eagon, Applications of the existence of big Cohen-Macaulay algebras, Adv. Math. (to appear). MR 1332808
- [HH4]
- Hochster, M., and J.A. Eagon, Tight closure in equal characteristic zero, in preparation.
- [HR]
- Hochster, M. and J.L. Roberts, Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay, Adv. Math. 13 (1974), 115--175. MR 347810
- [Ke]
- Kempf, G., The Hochster-Roberts theorem of invariant theory, Michigan Math. J. 26 (1979), 19--32. MR 514958
- [M1]
- Macaulay, F.S., The algebraic theory of modular systems, Cambridge Univ. Press, Cambridge, 1916. MR 1281612
- [M2]
- _____, Some properties of enumeration in the theory of modular systems, Proc. London Math. Soc. 26 (1927), 531--555.
- [Mum]
- Mumford, D., Algebraic geometry I complex projective varieties, Springer-Verlag, Berlin, Heidelberg, and New York, 1976. MR 453732
- [Mun]
- Munkres, J., Topological results in combinatorics, Michigan Math. J. 31 (1984), 113-128. MR 736476
- [PS1]
- Peskine, C. and L. Szpiro, Dimension projective finie et cohomologie locale, Inst. Hautes Études Sci. Publ. Math. 42 (1973), 323--395. MR 374130
- [PS2]
- _____, Syzygies et multiplicités, C. R. Acad. Sci. Paris Sér. A 278 (1974), 1421--1424. MR 349659
- [Re]
- Reisner, G., Cohen-Macaulay quotients of polynomial rings, Adv. Math. 21 (1976), 30--49. MR 407036
- [Ro1]
- Roberts, P., Le théorème d'intersection, C. R. Acad. Sc. Paris Sér. I Math. 304 (1987), 177--180. MR 880574
- [Ro2]
- _____, Intersection theorems, Math. Sci. Res. Inst. Publ., vol. 15, Springer-Verlag, New York, Berlin, and Heidelberg, 1989 pp.~417--436. MR 1015532
- [S]
- Serre J.-P., Algèbre locale. Multiplicités, Lecture Notes in Math., vol. 11, Springer-Verlag, Berlin, Heidelberg, and New York, 1965. MR 201468
- [St1]
- Stanley, R., Cohen-Macaulay rings and constructible polytopes, Bull. Amer. Math. Soc. 81 (1975), 135-142. MR 364231
- [St2]
- _____, The upper bound conjecture and Cohen-Macaulay rings, Stud. Appl. Math. 54 (1975), 133--142. MR 458437
- [St3]
- _____, The number of faces of a simplicial convex polytope, Adv. Math. 35 (1980), 236-238. MR 563925
Additional Information:
Reviewer(s):
Melvin
Hochster
Review Information:
Journal:
Bull. Amer. Math. Soc.
32
(1995),
265-275.
DOI:
10.1090/S0273-0979-1995-00577-X
PII:
S 0273-0979(1995)00577-X
|
Comments: webmaster@ams.org