Some remarks on n-absorbing subsemimodules.

Let R be a commutative semiring with 1 ≠ 0 , M an R-semimodule, and n ≥ 1 a positive integer. A proper subsemimodule P of M is called n-absorbing, if whenever r 1 , ... , r n ∈ R and x ∈ M together with r 1 ... r n x ∈ P , imply r 1 ... r n ∈ (P : M) or there exists 1 ≤ i ≤ n such that r 1 ... r i ^ ... r n x ∈ P . In this paper, we study the concept of n-absorbing subsemimodules that is a generalization of prime subsemimodules. Some basic properties of these subsemimodules and some useful examples of them are investigated. Also, we study the stability of n-absorbing subsemimodules with respect to some various constructions of semimodules. [ABSTRACT FROM AUTHOR]