Weakly approximaitly quasi-prime submodules and related concepts

الملخص EN

Let R be commutative Ring, and let T be unitary left R-module.

In this paper, WAPP-quasi prime submodules are introduced as new generalization of Weakly quasi prime submodules, where proper submodule C of an R-module T is called WAPP –quasi prime submodule of T, if whenever 0≠rstϵC, for r, s ϵR, t ϵT, implies that either r tϵ C +soc(T) or s tϵC +soc(T).

Many examples of characterizations and basic properties are given.

Furthermore several characterizations of WAPP-quasi prime submodules in the class of multiplication modules are unitary left R-module.

In this paper, WAPP-quasi prime submodules are introduced as new generalization of Weakly quasi prime submodules, where proper submodule C of an R-module T is called WAPP –quasi prime submodule of T, if whenever 0≠rstϵC, for r, s ϵR, t ϵT, implies that either r tϵ C +soc(T) or s tϵC +soc(T).

Many examples of characterizations and basic properties are given.

Furthermore several characterizations of WAPP-quasi prime submodules in the class of multiplication modules are established.