On the category of cofinite modules which is Abelian

Bahmanpour, Kamal; Naghipour, Reza; Sedghi, Monireh

doi:10.1090/S0002-9939-2014-11836-3

On the category of cofinite modules which is Abelian
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by Kamal Bahmanpour, Reza Naghipour and Monireh Sedghi PDF

Proc. Amer. Math. Soc. 142 (2014), 1101-1107 Request permission

Abstract:

Let $R$ denote a commutative Noetherian (not necessarily local) ring and $I$ an ideal of $R$ of dimension one. The main purpose of this paper is to generalize, and to provide a short proof of, K. I. Kawasaki’s theorem that the category $\mathscr {M}(R, I)_{cof}$ of $I$-cofinite modules over a commutative Noetherian local ring $R$ forms an Abelian subcategory of the category of all $R$-modules. Consequently, this assertion answers affirmatively the question raised by R. Hartshorne in his article Affine duality and cofiniteness [Invent. Math. 9 (1970), 145-164] for an ideal of dimension one in a commutative Noetherian ring $R$.

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