Gamma Comultiplication and Full Stability
Mehdi Sadiq Abbas, Balsam M. Hamad · IOP Conference Series Materials Science and Engineering · 2020
Abstract Let be a Γ-ring with identity (not necessarily commutative), and M a left RΓ-module. Then M is called fully stable if θ(N) ⊆ N for each RΓ-submodule N of M and RΓ-homomorphism θ from N into M. Equivalently, for each element m in M we have Rα 0 m = ϒ M α 0 ( ℓ R α 0 ( Rα 0 m ) ) , in other words, each α0-cyclic RΓ-submodule Rα0 m satisfies the double annihilator condition. In this paper we will introduce and study the notion of RΓ-modules in which every RΓ-submodule satisfies the double annihilator condition. Many properties and characterizations of this class of RΓ-modules are considering, and obtain some relatied results, as well as, their relationship with full stability.