Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2012.01.04
  • Published : 2013.03.31
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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).

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References

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