Some Results on Pure Submodules Relative to Submodule Shireen O. Dakheel|Noor R. Adeb

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Baghdad Science Journal

Abstract

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

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Journal BS. Some Results on Pure Submodules Relative to Submodule. BSJ [Internet]. 6Dec.2015 [cited 28May2020];12(4):833-7. Available from: http://bsj.uobaghdad.edu.iq/index.php/BSJ/article/view/2132
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