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      https://www.ias.ac.in/article/fulltext/pmsc/130/0001

    • Keywords

       

      Closed submodule; flat module; Dickson torsion theory; semiartinian module; proper class

    • Abstract

       

      A submodule $N$ of a module $M$ is called $\mathcal{D}$-closed if the socle of $M/N$ is zero. $\mathcal{D}$-closed submodules are similar to $\mathcal{S}$-closed submodules (a generalization of closed submodules) defined through nonsingular modules. First, we describe the smallest proper class (due to Buchsbaum) containing the class of short exact sequences determined by $\mathcal{D}$-closed submodules in terms of that submodule, and showthat it coincides with other classes of modules under certain conditions. Second, we study coprojective modules of this class, called edc-flat modules. We give some equivalent conditions for injective modules to be edc-flat for special rings, and for edc-flat modules to be projective (flat) for any ring.

    • Author Affiliations

       

      YILMAZ DURGUN1 SALAHATTIN ÖZDEMIR2

      1. Department of Mathematics, Çukurova University, Adana, Turkey
      2. Department of Mathematics, Dokuz Eylul University, Izmir, Turkey
    • Dates

       
  • Proceedings – Mathematical Sciences | News

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