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Graded strongly prime submodules over graded commutative rings | ||
| Journal of New Researches in Mathematics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 01 بهمن 1401 | ||
| نوع مقاله: research paper | ||
| شناسه دیجیتال (DOI): 10.30495/jnrm.2023.69642.2327 | ||
| نویسندگان | ||
Farkhondeh Farzalipour  ؛ Peyman Ghiasvand؛ Masoomeh Hezarjaribi Dastaki
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| Department of Mathematics, Payame Noor University, Tehran, Iran | ||
| چکیده | ||
| Let G be a group with identity e, R a graded ring and M a graded R-module. A proper graded submodule N of M is said to be graded strongly prime, if we have ((N+Rx_g):_RM)y_h⊆N, then x_g∈ N or y_h∈N for all x_g,y_h∈h(M). In this paper, we introduce the concept of graded strongly prime submodules as a generalization of graded prime submodules and we investigate some examples and basic properties of graded strongly prime submodules and state new results in this regard. In fact, in this article we show that the concept of graded strongly prime submodules is different from the concept of graded prime submodules. In continuing, we study the behavior of this structure module homomorphis, localization, quotient modules, Cartesian product. Finally, we state two kind of graded submodules of the amalgamation module along a graded ideal and investigate conditions under which they are graded strongly prime. | ||
| کلیدواژهها | ||
| Graded prime submodule؛ graded strongly prime submodule؛ graded strongly semiprime submodule | ||
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آمار تعداد مشاهده مقاله: 60 |
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