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Cominimaxness with respect to ideals of dimension one. (English) Zbl 1359.13017
Summary: 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 \(\mathcal{M}(R,I)_{com}\) 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 L. Melkersson [J. Algebra 372, 459–462 (2012; Zbl 1273.13029)]. 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.

MSC:
13D45 Local cohomology and commutative rings
14B15 Local cohomology and algebraic geometry
13E05 Commutative Noetherian rings and modules
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