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.
Keywords
T-pure submodule, T-pure essential submodule and T-pure closed submodule.
Article Type
Article
How to Cite this Article
Dakheel, Shireen O. and Adeb, Noor R.
(2015)
"Some Results on Pure Submodules Relative to Submodule,"
Baghdad Science Journal: Vol. 12:
Iss.
4, Article 23.
DOI: https://doi.org/10.21123/bsj.2015.12.4.833-837