On graded classical prime and graded prime submodules

Abstract

‎Let $G$ be a group with identity $e.$ Let $R$ be a $G$-graded‎ <br />‎commutative ring and $M$ a graded $R$-module‎. ‎In this paper‎, ‎we‎ <br />‎introduce several results concerning graded classical prime‎ <br />‎submodules‎. ‎For example‎, ‎we give a characterization of graded‎ <br />‎classical prime submodules‎. ‎Also‎, ‎the relations between graded‎ <br />‎classical prime and graded prime submodules of $M$ are studied‎.‎