GRADED SEMIPRIME SUBMODULES OVER NON-COMMUTATIVE GRADED RINGS | ||
| Journal of Algebraic Systems | ||
| دوره 10، شماره 1، آذر 2022، صفحه 95-110 اصل مقاله (177.38 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2021.9102.1442 | ||
| نویسندگان | ||
| P. Ghiasvand* ؛ F. Farzalipour | ||
| Department of Mathematics, Payame Noor University, P.O. Box 19395-3697, Tehran, Iran. | ||
| چکیده | ||
| Let $G$ be a group with identity $e$, $R$ be an associative graded ring and $M$ be a $G$-graded $R$-module. In this article, we intruduce the concept of graded semiprime submodules over non-commutative graded rings. First, we study graded prime $R$-modules over non-commutative graded rings and we get some properties of such graded modules. Second, we study graded semiprime and graded radical submodules of graded $R$-modules. For example, we give some equivalent conditions for a graded module to have zero graded radical submodule. | ||
| کلیدواژهها | ||
| graded prime module؛ graded radical submodule؛ graded semiprime submodule | ||
| مراجع | ||
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