FINITENESS PROPERTIES OF EXTENSION FUNCTORS OF COFINITE MODULES

Title & Authors
FINITENESS PROPERTIES OF EXTENSION FUNCTORS OF COFINITE MODULES
Irani, Yavar; Bahmanpour, Kamal;

Abstract
Let R be a commutative Noetherian ring, I an ideal of R and T be a non-zero I-cofinite R-module with dim(T) $\small{{\leq}}$ 1. In this paper, for any finitely generated R-module N with support in V(I), we show that the R-modules $\small{Ext^i_R}$(T,N) are finitely generated for all integers $\small{i{\geq}0}$. This immediately implies that if I has dimension one (i.e., dim R/I = 1), then $\small{Ext^i_R}$($\small{H^j_I}$(M), N) is finitely generated for all integers $\small{i}$, $\small{j{\geq}0}$, and all finitely generated R-modules M and N, with Supp(N) $\small{{\subseteq}}$ V(I).
Keywords
arithmetic rank;cofinite modules;local cohomology;minimax modules;
Language
English
Cited by
1.
Artinian cofinite modules over complete Noetherian local rings, Czechoslovak Mathematical Journal, 2013, 63, 4, 877
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