D-Extending Modules

Year 2020, Volume: 49 Issue: 3, 914 - 920, 02.06.2020

Yilmaz Durğun

https://doi.org/10.15672/hujms.460241

Cited By: 2

Abstract

A submodule $N$ of a module $M$ is called d-closed if $M/N$ has a zero socle. D-closed submodules are similar concept to s-closed submodules, which are defined through nonsingular modules by Goodearl. In this article we deal with modules with the property that all d-closed submodules are direct summands (respectively, closed, pure). The structure of a ring over which d-closed submodules of every module are direct summand (respectively, closed, pure) is studied.

Keywords

D-extending modules, d-closed submodules, semiartinian modules

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