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Generalizations of prime submodules over non-commutative rings | ||
| Journal of Hyperstructures | ||
| دوره 11، شماره 1، شهریور 2022، صفحه 65-83 اصل مقاله (334.23 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2023.2528 | ||
| نویسنده | ||
| Emel Aslankarayigit Ugurlu* | ||
| Department of Mathematics, Marmara University, P.O.Box 34722, Istanbul, Turkey | ||
| چکیده | ||
| Throughout this paper, R is an associative ring (not necessarily commutative) with identity and M is a right R-module with unitary. In this paper, we introduce a new concept of ∅-prime submodule over an associative ring with identity. Thus we define the concept as following: Assume that S(M) is the set of all submodules of M and Ø : S(M) ! S(M) [ f;g is a function. For every Y 2 S(M) and ideal I of R; a proper submodule X of M is called Ø-prime, if YI ⊆ X and YI ⊄ Ø(X); then Y ⊆ X or I ⊆ (X :R M): Then we examine the properties of Ø-prime submodules and characterize it when M is a multiplication module. | ||
| کلیدواژه‌ها | ||
| $\phi-$prime Submodule؛ Non-commutative Ring؛ Multiplication Module | ||
| مراجع | ||
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