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)

Journals Home Search My Subscriptions Subscribe
Previous issue | This issue | Most recent issue | All issues (1950–Present) | Next issue | Previous article | Articles in press | Recently published articles | Next article
Request Permissions
 
 

 

Descent of the canonical module in rings with the approximation property


Author: Christel Rotthaus
Journal: Proc. Amer. Math. Soc. 124 (1996), 1713-1717
MSC (1991): Primary 13B35, 13B40, 13D45, 13F40, 13J15
DOI: https://doi.org/10.1090/S0002-9939-96-03244-3
MathSciNet review: 1307562
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $(R,m)$ be a local Noetherian Cohen-Macaulay ring with the approximation property. We show that $R$ admits a canonical module.

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

  • [A] M. Artin, Algebraic approximation of structures over complete local rings, Inst. Hautes Études Sci. Publ. Math. 36 (1969), 23–58. MR 268188
  • [H] V. Hinich, Rings with approximation property admit a dualizing complex, Math. Nachr. 163 (1993), 289–296. MR 1235073, https://doi.org/10.1002/mana.19931630124
  • [HK] F. Herzog and E. Kunz, Der kanonische Modul eines Cohen-Macaulay Rings, Lecture Notes in Math., vol. 238, Springer, New York, 1971.
  • [M] Hideyuki Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics, vol. 8, Cambridge University Press, Cambridge, 1986. Translated from the Japanese by M. Reid. MR 879273
  • [R] C. Rotthaus, Divisorial ascent in rings with the approximation property, J. of Algebra 178 (1995), 541--560.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 13B35, 13B40, 13D45, 13F40, 13J15

Retrieve articles in all journals with MSC (1991): 13B35, 13B40, 13D45, 13F40, 13J15

Additional Information

Christel Rotthaus
Affiliation: Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
Email: rotthaus@mth.msu.edu

DOI: https://doi.org/10.1090/S0002-9939-96-03244-3
Keywords: Canonical modules, dualizing complexes, Cohen-Macaulay rings, approximation property, excellent local Henselian rings
Received by editor(s): September 16, 1994
Received by editor(s) in revised form: December 14, 1994
Additional Notes: The author gratefully acknowledges partial support from the National Science Foundation
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1996 American Mathematical Society