On classical n-absorbing submodules

Abstract

In this paper, we introduce the notion of classical n-absorbing submodules of a module M over a commutative ring R with identity, which is a generalization of classical prime submodules. A proper submodule N of M is said to be classical n-absorbing if whenever a₁a₂... a_n+1 m in M, for a₁a₂... a_n+1 in R and m in M, then there are n of the a_i's whose product with m is in N. We give some basic results concerning classical n-absorbing submodules. Then the classical n-absorbing avoidance theorem for submodules is proved. Finally, classical n-absorbing submodules in several classes of modules are studied.