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Keywords
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Associated prime, cofinite module, local cohomology, minimax module, regular ring,
weakly Laskerian module
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Abstract
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Let a denote an ideal in a regular local (Noetherian) ring R and let N be a finitely generated Rmodule
with support in V (a). The purpose of this paper is to show that all homomorphic images of the R-modules
Extj
R(N,Hia
(R)) have only finitely many associated primes, for all i, j ≥ 0, whenever dimR ≤ 4 or dimR/a ≤
3 and R contains a field. In addition, we show that if dimR = 5 and R contains a field, then the R-modules
Extj
R(N,Hia
(R)) have only finitely many associated primes, for all i, j ≥ 0.
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