SOME RESULTS ON STRONGLY PRIME SUBMODULES

Document Type : Original Manuscript

Author

Department of Mathematics, Shahrekord University, P.O.Box 115, Shahrekord, Iran.

Abstract

Let R be a commutative ring with identity and let M be an R-module. A proper submodule P of M is called strongly prime submodule if (P+Rx:M)yP for x,yM, implies that xP or yP. In this paper, we study more properties of strongly prime submodules. It is shown that a finitely generated R-module M is Artinian if and only if M is Noetherian and every strongly prime submodule of M is maximal. We also study the strongly dimension of a module
which is defined to be the length of a longest chain of strongly prime submodules.

Keywords