D-Extending Modules

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Hacettepe Journal of Mathematics and Statistics
Volume:49 Issue:3
D-Extending Modules

D-Extending Modules

Pages : 914-920

View : 14 | Download : 5

Publication Date : 2020-06-02

Article Type : Research Paper

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 insert ignore into journalissuearticles values(respectively, closed, pure);. The structure of a ring over which d-closed submodules of every module are direct summand insert ignore into journalissuearticles values(respectively, closed, pure); is studied.
Keywords : D extending modules, d closed submodules, semiartinian modules

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