On Essential (Complement) Submodules with Respect to an Arbitrary Submodule

E. A. Al-Dhaheri --- B. H. Al-Bahrani

Iraqi Journal of Science المجلة العراقية للعلوم
ISSN: 00672904/23121637 Year: 2018 Volume: 59 Issue: 2B Pages: 904-908
Publisher: Baghdad University جامعة بغداد


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


Essential submodules --- T-essential submodules