• A Generalization of the Finiteness Problem in Local Cohomology Modules

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/119/02/0159-0164

    • Keywords

       

      Local cohomology modules; cofiniteness; weakly Laskerian; spectral sequences.

    • Abstract

       

      Let $\mathfrak{a}$ be an ideal of a commutative Noetherian ring 𝑅 with non-zero identity and let 𝑁 be a weakly Laskerian 𝑅-module and 𝑀 be a finitely generated 𝑅-module. Let 𝑡 be a non-negative integer. It is shown that if $H^i_{\mathfrak{a}}(N)$ is a weakly Laskerian 𝑅-module for all $i < t$, then $\mathrm{Hom}_R(R/\mathfrak{a},H^t_{\mathfrak{a}}(M, N))$ is weakly Laskerian 𝑅-module. Also, we prove that $\mathrm{Ext}^i_R(R/\mathfrak{a},H^t_{\mathfrak{a}}(N))$ is weakly Laskerian 𝑅-module for all $i=0,1$. In particular, if $\mathrm{Supp}_R(H^i_{\mathfrak{a}}(N))$ is a finite set for all $i < t$, then $\mathrm{Ext}^i_R(R/\mathfrak{a},H^t_{\mathfrak{a}}(N))$ is weakly Laskerian 𝑅-module for all $i=0,1$.

    • Author Affiliations

       

      Amir Mafi1 2

      1. Department of Mathematics, University of Kurdistan, P.O. Box 416, Sanandaj, Iran
      2. Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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