ON WEAKLY QUASI n-ABSORBING SUBMODULES

ON WEAKLY QUASI n-ABSORBING SUBMODULES

Let R be a commutative ring with 1 ≠ 0, n be a positive integer and M be an R-module. In this paper, we introduce the concept of weakly quasi n-absorbing submodule which is a proper generalization of quasi n-absorbing submodule. We define a proper submodule N of M to be a weakly quasi n-absorbing submodule if whenever a ∈ R and x ∈ M with 0 ≠ aⁿ x ∈ N, then aⁿ ∈ (N :_R M) or a^n-1 x ∈ N. We study the basic properties of this notion and establish several characterizations.

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