D-Extending Modules

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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