- All Journals
- Al-Qadisiyah University
- Basrah University
- Kirkuk University
- Mosul University
- The Iraqi Borad for Medical Specialization
- University of Anbar
- University of Technology
- Al Mustafa University
- Al-Zahraa University for Women
- Alnoor University
- Kunooz University
- Misan University
- Ninevah University
- Tikrit University
- University of Al-Hamdaniya
- University of Kerbala
Some Results on Pure Submodules Relative to Submodule | ||
| Baghdad Science Journal | ||
| Article 1, Volume 12, Issue 4, 2015, Pages 833-837 | ||
| Authors | ||
| Shireen O. Dakheel; Noor R. Adeb | ||
| 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 | ||
| pure submodule; pure essential submodule and T; pure closed submodule | ||
|
Statistics Article View: 125 PDF Download: 110 |
||