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
Abstract | References | Similar Articles | Additional Information
Abstract: Let 
be a local Noetherian Cohen-Macaulay ring with the approximation property. We show that 
admits a canonical module.
- [A] M. Artin, Algebraic approximation of structures over complete local rings, Publ. Math. IHES, 36, (1969), 23--58. MR 42:3087
- [H] V. Hinich, Rings with approximation property admit a dualizing complex, Math. Nachr. 163 (1993), 289--296. MR 94h:13017
- [HK] F. Herzog and E. Kunz, Der kanonische Modul eines Cohen-Macaulay Rings, Lecture Notes in Math., vol. 238, Springer, New York, 1971.
- [M] H. Matsumura, Commutative ring theory, Cambridge University Press, Cambridge, 1986. MR 88h:13001
- [R] C. Rotthaus, Divisorial ascent in rings with the approximation property, J. of Algebra 178 (1995), 541--560.
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
