On fully semiprime submodules and fully semiprime modules

Abstract EN

Let R be a commutative ring with unity and let M be a unitary R-module.

In this paper we study fully semi prime sub modules and fully semi prime modules, where a proper fully invariant R-sub module W of M is called fully semi prime in M if whenever X*XW for all fully invariant R-sub module X of M, implies XW.

M is called fully semi prime if (0) is a fully semi prime sub module of M.

We give basic properties of these concepts.

Also we study the relationships between fully semi prime sub modules (modules) and other related sub modules (modules) respectively.