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.
Primary Language | English |
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Subjects | Mathematical Sciences |
Journal Section | Mathematics |
Authors | |
Publication Date | June 2, 2020 |
Published in Issue | Year 2020 Volume: 49 Issue: 3 |