R-annihilator-Coessential and R-annihilator-Coclosed Submodules.

Let W be a unitary left R-module on associative ring R with identity. A submodule F of W is called R-annihilator small if F+T=W, where T is a submodule of W, implies that ann(T)=0, where ann(T) indicates annihilator of T in R. In this paper, we introduce the concepts of R-annihilator-coessential and R- annihilator - coclosed submodules. We give many properties related with these types of submodules. [ABSTRACT FROM AUTHOR]