Bulletin of the
Korean Mathematical Society BKMS

Let $R$ be a commutative ring with $1\neq 0$, $n$ 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 $a\in R$ and $x\in M$ with $0\neq a^{n}x\in N,$ then $a^{n}\in (N:_{R}M)$ or $a^{n-1}x\in N.$ We study the basic properties of this notion and establish several characterizations.

Keywords: Quasi $n$-absorbing submodule, weakly quasi $n$-absorbing submodule

MSC numbers: Primary 13A15, 13B02