Moharram Aghapournahr: Abelian category of cominimax modules and local cohomology, 219-231

Abstract:

Let $R$ be a commutative Noetherian ring, ${\mathfrak{a}}$ an ideal of $R$, $M$ an arbitrary $R$-module and $X$ a finite $R$-module. We prove that the category of ${\mathfrak{a}}$-cominimax modules is a Melkersson subcategory of $R$-modules whenever $\dim R\leq 1$ and is an Abelian subcategory whenever $\dim R\leq 2$. We prove a characterization theorem for ${\operatorname{H}}_{{\mathfrak{a}}}^{i}(M)$ and ${\operatorname{H}}_{{\mathfrak{a}}}^{i}(X,M)$ to be ${{\mathfrak{a}}}$-cominimax for all $i$, whenever one of the following cases holds: (a) ${\operatorname{ara}} ({\mathfrak{a}})\leq 1$, (b) $\dim R/{\mathfrak{a}} \leq 1$ or (c) $\dim R\leq 2$.

Key Words: Local cohomology, minimax modules, cominimax modules, Melkersson subcategory, Abelian category.

2020 Mathematics Subject Classification: Primary 13D45; Secondary 13E05, 14B15.

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