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Purely Quasi-Dedekind Modules And Purely Prime Modules | ||
| journal of al-qadisiyah for pure science(quarterly) | ||
| Article 1, Volume 11, Issue 4, 2011, Pages 30-45 PDF (0 K) | ||
| Authors | ||
| ; ar Younis Ghawi | ||
| Abstract | ||
| An R-submodule N of an R-module M is called pure if for every ideal I of R . In this paper we introduce the notion of purely quasi-invertible submodule and a purely quasi-Dedekind module, where an R-submodule N of an R-module M is called purely quasi-invertible if, N is pure and . And an R-module M is called purely quasi-Dedekind if, every nonzero pure submodule N of M is quasi-invertible ; that is . Beside these, we also introduce the notion of purely prime module, where an R-module M is called purely prime module if for all nonzero pure submodule N of M .We gave many properties related with this concepts. And we studied the relationships between these concepts and several other types of modules. In this paper R is a commutative ring with unity and M is a unitary R-module . | ||
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