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Cousin complexes and generalized fractions

Published online by Cambridge University Press:  18 May 2009

Adrian M. Riley ,
Rodney Y. Sharp  and
Hossein Zakeri
Adrian M. Riley
Affiliation:
Department of Pure Mathematics, The University of Sheffield, Hicks Building, Sheffield S3 7RH, England
Rodney Y. Sharp
Affiliation:
Department of Pure Mathematics, The University of Sheffield, Hicks Building, Sheffield S3 7RH, England
Hossein Zakeri
Affiliation:
Department of Mathematics, University for Teacher Education, 49 Mobarezan Avenue, Tehran, Iran
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Let A be a commutative Noetherian ring (with non-zero identity). The Cousin complex C(A) for A is described in [6, §2]: it is a complex of A-modules and A-homomorphisms

with the property that, for each n≥0,

Cohen-Macaulay rings may be characterized in terms of the Cousin complex: A is a Cohen-Macaulay ring if and only if C(A) is exact [6, (4.7)]. Also the Cousin complex provides a natural minimal injective resolution for a Gorenstein ring: see [6, (5.4)].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 26 , Issue 1 , January 1985 , pp. 51 - 67
Copyright
Copyright © Glasgow Mathematical Journal Trust 1985

References

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