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2017•Journal of Algebra and Its ApplicationsRequires access

Regular sequences and vanishing of the homological functors

Kamal Bahmanpour

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Abstract

Let [Formula: see text] be a Noetherian local ring of dimension [Formula: see text] and let [Formula: see text] be a nonzero finitely generated [Formula: see text]-module. Let [Formula: see text] be a positive integer and let [Formula: see text] be an [Formula: see text]-regular sequence. In this paper we shall present some equivalent conditions for the vanishing of the [Formula: see text]-modules [Formula: see text] and [Formula: see text].

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What this paper is about

Let [Formula: see text] be a Noetherian local ring of dimension [Formula: see text] and let [Formula: see text] be a nonzero finitely generated [Formula: see text]-module. Let [Formula: see text] be a positive integer and let [Formula: see text] be an [Formula: see text]-regular sequence. In this paper we shall present some equivalent conditions for the vanishing of the [Formula: see text]-modules [Formula: see text] and [Formula: see text].

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Available abstract

Let [Formula: see text] be a Noetherian local ring of dimension [Formula: see text] and let [Formula: see text] be a nonzero finitely generated [Formula: see text]-module. Let [Formula: see text] be a positive integer and let [Formula: see text] be an [Formula: see text]-regular sequence. In this paper we shall present some equivalent conditions for the vanishing of the [Formula: see text]-modules [Formula: see text] and [Formula: see text].

Key concepts: Mathematics, Noetherian ring, Noetherian, Dimension (graph theory), Local ring, Functor, Finitely-generated abelian group, Integer (computer science)

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