• YILMAZ DURGUN

      Articles written in Proceedings – Mathematical Sciences

    • On $\mathcal{D}$-closed submodules

      YILMAZ DURGUN SALAHATTIN ÖZDEMIR

      More Details Abstract Fulltext PDF

      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.

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