[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2013.50.2.649

FINITENESS PROPERTIES OF EXTENSION FUNCTORS OF COFINITE MODULES

Irani, Yavar (Department of Mathematics Islamic Azad University Meshkin-Shahr branch)
Bahmanpour, Kamal (Department of Mathematics Islamic Azad University-Ardabil branch)

Publication Information

Bulletin of the Korean Mathematical Society / v.50, no.2, 2013 , pp. 649-657 More about this Journal

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) ${\leq}$ 1. In this paper, for any finitely generated R-module N with support in V(I), we show that the R-modules $Ext^i_R$ (T,N) are finitely generated for all integers $i{\geq}0$ . This immediately implies that if I has dimension one (i.e., dim R/I = 1), then $Ext^i_R$ ( $H^j_I$ (M), N) is finitely generated for all integers $i$ , $j{\geq}0$ , and all finitely generated R-modules M and N, with Supp(N) ${\subseteq}$ V(I).

Keywords

arithmetic rank; cofinite modules; local cohomology; minimax modules;

Citations & Related Records

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