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Modules whose finiteness dimensions coincide with their cohomological dimensions

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Abstract Let a be an ideal of a commutative Noetherian ring R with identity. We study finitely generated R-modules M whose a -finiteness and a -cohomological dimensions are equal. In… Click to show full abstract

Abstract Let a be an ideal of a commutative Noetherian ring R with identity. We study finitely generated R-modules M whose a -finiteness and a -cohomological dimensions are equal. In particular, we examine relative analogues of quasi-Buchsbaum, Buchsbaum and surjective Buchsbaum modules. We reveal several interactions between these types of modules that extend some of the existing results in the classical theory to the relative one.

Keywords: whose finiteness; finiteness dimensions; modules whose; coincide cohomological; dimensions coincide; cohomological dimensions

Journal Title: Journal of Pure and Applied Algebra
Year Published: 2021

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