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Descent of the canonical module in rings with the approximation property
Author(s):
Christel
Rotthaus
Journal:
Proc. Amer. Math. Soc.
124
(1996),
1713-1717.
MSC (1991):
Primary 13B35, 13B40, 13D45, 13F40, 13J15
MathSciNet review:
1307562
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Abstract:
Let  be a local Noetherian Cohen-Macaulay ring with the approximation property. We show that  admits a canonical module.
References:
- [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.
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Additional Information:
Christel
Rotthaus
Affiliation:
Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027
Email:
rotthaus@mth.msu.edu
DOI:
10.1090/S0002-9939-96-03244-3
PII:
S 0002-9939(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
Copyright of article:
Copyright
1996,
American Mathematical Society
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