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    • On 𝑃-Coherent Endomorphism Rings

      Li-Xin Mao

      Volume 118 Issue 4 November 2008 pp 557-567

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/118/04/0557-0567

    • Keywords

       

      𝑃-coherent ring; $PP$ ring; torsionfree module; divisible module; precover; preenvelope; pseudokernel; pseudocokernel.

    • Abstract

       

      A ring is called right 𝑃-coherent if every principal right ideal is finitely presented. Let $M_R$ be a right 𝑅-module. We study the 𝑃-coherence of the endomorphism ring 𝑆 of $M_R$. It is shown that 𝑆 is a right 𝑃-coherent ring if and only if every endomorphism of $M_R$ has a pseudokernel in add $M_R; S$ is a left 𝑃-coherent ring if and only if every endomorphism of $M_R$ has a pseudocokernel in add $M_R$. Some applications are given.

    • Author Affiliations

       

      Li-Xin Mao1

      1. Institute of Mathematics, Nanjing Institute of Technology, Nanjing 211167, People’s Republic of China

    • Dates

       
      Published
      November 2008
      Manuscript received
      22 April 2007
      Manuscript revised
      19 May 2008

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