On classical n-absorbing submodules

  • Reza Nikandish Jundi-Shapur University of Technology, Iran
  • M. J. Nikmehr K.N. Toosi University of Technology, Iran
  • A. Yassine K.N. Toosi University of Technology, Iran


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... an+1 m in M, for a1a2... an+1 in R and m in M, then there are n of the ai'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.