On (k,n)-closed submodules.

Let R be a commutative ring with 1 ≠ 0 and M an R-module. We will call a proper submodule N of M as a semi n-absorbing submodule of M if whenever r∊R, m∊M with rnm∊N, then rn∊(N:R M) or rn-1m∊N. We will say N to be a (k, n)-closed submodule of M if whenever r∊R, m∊M with rkm∊N, then rn∊(N:R M) or rn-1m∊N. In this paper we introduce semi n-absorbing and (k, n)-closed submodules of modules over commutative rings, and investigate their basic properties. [ABSTRACT FROM AUTHOR]