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 show that 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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Durǧun, Y., Özdemir, S. On \(\varvec{\mathcal {D}}\)-closed submodules. Proc Math Sci 130, 1 (2020). https://doi.org/10.1007/s12044-019-0537-1
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DOI: https://doi.org/10.1007/s12044-019-0537-1