Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the Cohen-Macaulay modules of graded subrings

Author: Douglas Hanes
Journal: Trans. Amer. Math. Soc. 357 (2005), 735-756
MSC (2000): Primary 13C14
Published electronically: April 27, 2004
MathSciNet review: 2095629
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We give several characterizations for the linearity property for a maximal Cohen-Macaulay module over a local or graded ring, as well as proofs of existence in some new cases. In particular, we prove that the existence of such modules is preserved when taking Segre products, as well as when passing to Veronese subrings in low dimensions. The former result even yields new results on the existence of finitely generated maximal Cohen-Macaulay modules over non-Cohen-Macaulay rings.

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

  • 1. J. Backelin, J. Herzog, and B.Ulrich, Linear maximal Cohen-Macaulay modules over strict complete intersections, J. of Pure and Appl. Algebra 71 (1991), 187-202. MR 92g:13011
  • 2. J. Brennan, J. Herzog, and B. Ulrich, Maximally generated Cohen-Macaulay modules, Math. Scand. 61 (1987), 181-203. MR 89j:13027
  • 3. W. Bruns and J. Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics, 39, Cambridge University Press, Cambridge, 1993. MR 95h:13020
  • 4. J. Eagon and M. Hochster, Cohen-Macaulay rings, invariant theory, and the generic perfection of determinantal loci, Amer. J. Math. 93 (1971), 1020-1058. MR 46:1787
  • 5. J. Eagon and D.G. Northcott, Generically acyclic complexes and generically perfect ideals, Proc. Royal Soc., Series A 299 (1967), 147-172. MR 35:5435
  • 6. D. Eisenbud and F.-O. Schreyer (App. by J. Weyman), Resultants and Chow forms via exterior syzygies, J. Amer. Math. Soc. 16 (2003), 537-579.
  • 7. S. Goto and K. Watanabe, On graded rings, I, J. Math. Soc. Japan 30 (1978), 179-213. MR 81m:13021
  • 8. D. Hanes, Special conditions on maximal Cohen-Macaulay modules, and applications to the theory of multiplicities, Thesis, University of Michigan, 1999.
  • 9. -, Length approximations for independently generated ideals, J. Algebra 237 (2001), 708-718. MR 2001m:13006
  • 10. M. Hochster, Big Cohen-Macaulay modules and algebras and embeddability in rings of Witt vectors, Queen's Papers Pure and Appl. Math. 42 (1975), 106-195. MR 53:407
  • 11. -, Topics in the homological theory of modules over commutative rings, CBMS Regional Conference Series in Mathematics, No. 24. American Mathematical Society, Providence, RI, 1975. MR 51:8096
  • 12. C. Huneke and M. Miller, A note on the multiplicity of Cohen-Macaulay algebras with pure resolutions, Canadian J. of Math. 37 (1985), 1149-1162. MR 87d:13024
  • 13. C. Lech, Note on multiplicities of ideals, Arkiv for Math. 4 (1960), 63-86. MR 25:3955
  • 14. F. Ma, Splitting in integral extensions, Cohen-Macaulay modules and algebras, J. Algebra 116 (1988), 176-195. MR 89e:13010
  • 15. D.G. Northcott and D. Rees, Reductions of ideals in local rings, Proc. Camb. Phil. Soc. 50 (1954), 145-158. MR 15:596a
  • 16. C. Peskine and L. Szpiro, Notes sur un air de H. Bass, Unpublished preprint, Brandeis University.
  • 17. B. Ulrich, Gorenstein rings and modules with high numbers of generators, Math. Z. 188 (1984), 23-32. MR 85m:13021

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 13C14

Retrieve articles in all journals with MSC (2000): 13C14

Additional Information

Douglas Hanes
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Address at time of publication: Neuro-otology Research, Legacy Research Center, 1225 NE 2nd Avenue, Portland, Oregon 97232

Received by editor(s): November 11, 2001
Received by editor(s) in revised form: August 14, 2003
Published electronically: April 27, 2004
Article copyright: © Copyright 2004 American Mathematical Society

American Mathematical Society