- 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
On Essential (Complement) Submodules with Respect to an Arbitrary Submodule | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 59, Issue 2, 2018, Pages 904-908 | ||
| Authors | ||
| E. A. Al-Dhaheri; B. H. Al-Bahrani | ||
| Abstract | ||
| In this paper we Proved other properties of essential and complement submodules to an arbitrary submodule of an R-module M .We prove that for a family {Mα}α ∊ʌ of modules . If Tα and Nα are submodules of Mα with N α +T α ≤T α-e M α ,∀ α, then ⨁α∊ʌ (Nα +Tα)≤⨁ α ∊ʌ Tα –e ⨁α ∊ʌ Mα. Also we show that for submodules T, A, B and C of a module M such that T ≤ A ≤ C. If B is T- c for A in M and C is T- c for B in M , then C is maximal T- essential extension of A in M | ||
| Keywords | ||
| Essential submodules; essential submodules | ||
|
Statistics Article View: 169 PDF Download: 39 |
||