Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On Gorenstein ideals of codimension four

Authors: W. V. Vasconcelos and R. Villarreal
Journal: Proc. Amer. Math. Soc. 98 (1986), 205-210
MSC: Primary 13H10; Secondary 13C15, 13D99
MathSciNet review: 854019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We describe two computations showing how the Koszul homology impacts on the structure of Cohen-Macaulay ideals of height 3 and Gorenstein ideals of height 4.

References [Enhancements On Off] (What's this?)

  • [AB] M. Auslander and M. Bridger, Stable module theory, Mem. Amer. Math. Soc. no. 94 (1969). MR 0269685 (42:4580)
  • [AH] L. Avramov and J. Herzog, The Koszul algebra of a codimension two embedding, Math. Z. 175 (1980), 249-260. MR 602637 (82g:13011)
  • [BE] D. Buchsbaum and D. Eisenbud, Algebra structures for finite free resolutions and some structure theorems for ideals of codimension 3, Amer. J. Math. 99 (1977), 447-485. MR 0453723 (56:11983)
  • [BU] R. O. Buchweitz and B. Ulrich, Homological properties which are invariant under linkage, preprint, 1983.
  • [He] J. Herzog, Deformation von Cohen-Macaulay algebren, J. Reine Angew. Math. 318 (1980), 83-105. MR 579384 (81m:13012)
  • [HKu] J. Herzog and M. Kühl, On the Betti numbers of finite pure and linear resolutions, Comm. Algebra 12 (1984), 1627-1646. MR 743307 (85e:13021)
  • [HK] J. Herzog and E. Kunz, Der kanonische Modul eines Cohen-Macaulay rings, Lecture Notes in Math., vol. 283, Springer-Verlag, Berlin and New York, 1971. MR 0412177 (54:304)
  • [HM] J. Herzog and M. Miller, Gorenstein ideals of deviation two, Comm. Algebra 13 (1985), 1977-1990. MR 795487 (87b:13027)
  • [HVV] J. Herzog, W. V. Vasconcelos and R. Villarreal, Ideals with sliding depth, Nagoya Math. J. 99 (1985), 159-172. MR 805087 (86k:13022)
  • [HSV] J. Herzog, A. Simis and W. V. Vasconcelos, On the arithmetic of algebras of linear type, Trans. Amer. Math. Soc. 283 (1984), 661-683. MR 737891 (86a:13015)
  • [Hu$ _{1}$] C. Huneke, Linkage and the Koszul homology of ideals, Amer. J. Math. 104 (1982), 1043-1062. MR 675309 (84f:13019)
  • [Hu$ _{2}$] -, Determinantal ideals of linear type, preprint, 1985.
  • [HuM] C. Huneke and M. Miller, A note on the multiplicity of Cohen-Macaulay algebras with pure resolutions, Canad. J. Math. (to appear). MR 828839 (87d:13024)
  • [KM] A. Kustin and M. Miller, Deformation and linkage of Gorenstein algebras, Trans. Amer. Math. Soc. 284 (1984), 501-534. MR 743730 (85k:13015)
  • [Le$ _{1}$] K. Lebelt, Zur homologischen dimension äußerer Potenzen von Moduln, Arch. Math. 26 (1975), 595-601. MR 0396534 (53:397)
  • [Le$ _{2}$] -, Freie Auflösungen äußerer Potenzen, Manuscripta Math. 21 (1977), 341-355. MR 0450253 (56:8549)
  • [SV] A. Simis and W. V. Vasconcelos, The syzygies of the conormal module, Amer. J. Math. 103 (1981), 203-224. MR 610474 (82i:13016)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13H10, 13C15, 13D99

Retrieve articles in all journals with MSC: 13H10, 13C15, 13D99

Additional Information

Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society