• On $\mathcal{D}$-closed submodules

• # Fulltext

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

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

• # Proceedings – Mathematical Sciences

Volume 130, 2020
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019