On the extension functors of certain modules of small dimension

Articles in Press

Document Type : Research Paper

Authors

Department of Basic Sciences, Arak University of Technology, P. O. Box 38135-1177, Arak, Iran.

Abstract

Let $R$ be a commutative Noetherian ring with nonzero identity, $I$ an ideal of $R$, and $M$ an $R$-module such that ${\rm Ext}^i_R(R/I,M)$ is minimax for all $i\leq \dim M$. We prove that if ${\rm Supp}_R(M)\subseteq V(I)$, then for every finitely generated $R$-module $N$ with $\dim N/IN \leq 1$, the $R$-module ${\rm Ext}^i_R(N,M)$ is $I$-cominimax for all $i\geq 0$. In particular, for a finitely generated $R$-module $N$ with ${\rm Supp}_R (N/IN)\subseteq {\rm Max}(R)$, we show that ${\rm Ext}^i_R (N,M)$ is Artinian and $I$-cofinite for all $i \geq 0$.

Keywords

References

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Algebraic Structures and Their Applications

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