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Generalized fractions and Hughes' gradetheoretic analogue of the Cousin complex

Published online by Cambridge University Press:  18 May 2009

R. Y. Sharp  and
M. Yassi
R. Y. Sharp
Affiliation:
Department of Pure MathematicsUniversity of SheffieldHicks Building Sheffield S3 7RH
M. Yassi
Affiliation:
Department of Pure MathematicsUniversity of SheffieldHicks Building Sheffield S3 7RH
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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 [19, Section 2]: it is a complex of A-modules and A-homomorphisms

with the property that, for each n ∈ N0 (we use N0 to denote the set of non-negative integers),

Cohen–Macaulay rings can be characterized in terms of the Cousin complex: A is a Cohen–Macaulay ring if and only if C(A) is exact [19, (4.7)]. Also, the Cousin complex provides a natural minimal injective resolution for a Gorenstein ring (see [19,(5.4)]).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 32 , Issue 2 , May 1990 , pp. 173 - 188
Copyright
Copyright © Glasgow Mathematical Journal Trust 1990

References

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