Cominimaxness with respect to ideals of dimension one
Bull. Korean Math. Soc. 2017 Vol. 54, No. 1, 289-298
Published online November 3, 2016
Printed January 31, 2017
Yavar Irani
Islamic Azad University Meshkin-Shahr Branch
Abstract : Let $R$ denote a commutative Noetherian (not necessarily local) ring and let $I$ be an ideal of $R$ of dimension one. The main purpose of this note is to show that the category $\mathscr{M}(R, I)_{com}$ of $I$-cominimax $R$-modules forms an Abelian subcategory of the category of all $R$-modules. This assertion is a generalization of the main result of Melkersson in \cite{Me}. As an immediate consequence of this result we get some conditions for cominimaxness of local cohomology modules for ideals of dimension one. Finally, it is shown that the category $\mathcal{C}_{B}^1(R)$ of all $R$-modules of dimension at most one with finite Bass numbers forms an Abelian subcategory of the category of all $R$-modules.
Keywords : arithmetic rank, Bass number, cominimax modules, minimax modules
MSC numbers : 13D45, 14B15, 13E05
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