R. Abu-Dawwas
Yarmouk University, Irbid , Jordan
[ 1 ] - On graded classical prime and graded prime submodules
Let $G$ be a group with identity $e.$ Let $R$ be a $G$-graded commutative ring and $M$ a graded $R$-module. In this paper, we introduce several results concerning graded classical prime submodules. For example, we give a characterization of graded classical prime submodules. Also, the relations between graded classical prime and graded prime submodules of $M$ are studied.
[ 2 ] - On Graded Weakly Classical Prime Submodules
Let R be a G-graded ring and M be a G-graded R-module. In this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.
[ 3 ] - Graded r-Ideals
Let $G$ be a group with identity $e$ and $R$ be a commutative $G$-graded ring with nonzero unity $1$. In this article, we introduce the concept of graded $r$-ideals. A proper graded ideal $P$ of a graded ring $R$ is said to be graded $r$-ideal if whenever $a, bin h(R)$ such that $abin P$ and $Ann(a)={0}$, then $bin P$. We study and investigate the behavior of graded $r$-ideals to introduce ...
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