Open AccessOn generalizations of graded multiplication modules
Author(s) -
Rashid Abu-Dawwas,
Hicham Saber,
Tariq Alraqad,
Reem Jaradat
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.51241
Subject(s) - multiplication (music) , mathematics , graded ring , ideal (ethics) , prime (order theory) , arithmetic , pure mathematics , algebra over a field , combinatorics , philosophy , epistemology
Let $G$ be a group with identity $e$, $R$ be a $G$-graded ring with unity $1$ and $M$ be a $G$-graded $R$-module. In this article, we introduce the concept of graded quasi multiplication modules, where graded $M$ is said to be graded quasi multiplication if for every graded weakly prime $R$-submodule $N$ of $M$, $N=IM$ for some graded ideal $I$ of $R$. Also, we introduce the concept of graded absorbing multiplication modules; $M$ is said to be graded absorbing multiplication if $M$ has no graded $2$-absorbing $R$-submodules or for every graded $2$-absorbing $R$-submodule $N$ of $M$, $N=IM$ for some graded ideal $I$ of $R$. We prove many results concerning graded weakly prime submodules and graded $2$-absorbing submodules that will be useful in providing several properties of the two classes of graded quasi multiplication modules and graded absorbing multiplication modules.