R-Prime Submodules

Abstract

Let $R$ be a commutative ring with unity and $K$ be a submodule of a non-zero left $R$-module $D$. This paper introduces a new concept as a generalization of the prime submodule, which is called $R$-prime. We prove some properties of the $R$-prime submodule and study the relationship between the $R$-prime submodules and other submodules as prime and $J$-semiprime. Also, we will see the $R$-prime submodule with the multiplication module and the injective envelope.