منابع مشابه
2-absorbing $I$-prime and 2-absorbing $I$-second submodules
Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we will introduce the notions of 2-absorbing $I$-prime and 2-absorbing $I$-second submodules of an $R$-module $M$ as a generalization of 2-absorbing and strongly 2-absorbing second submodules of $M$ and explore some basic properties of these classes of modules.
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Let L be a complete lattice. We introduce and characterize the prime L-submodules of a unitary module over a commutative ring with identity. Finally, we investigate the Zariski topology on the prime L-Spectrum of a unitary module, consisting of the collection of all prime L-submodules, and prove that for L-top modules the Zariski topology on L-Spec(M) exists. © 2007 Elsevier B.V. All rights res...
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Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. A proper submodule $P$ of $M$ is called strongly prime submodule if $(P + Rx : M)ysubseteq P$ for $x, yin M$, implies that $xin P$ or $yin P$. In this paper, we study more properties of strongly prime submodules. It is shown that a finitely generated $R$-module $M$ is Artinian if and only if $M$ is Noetherian and every st...
متن کاملOn 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.
متن کاملOn Generalization of prime submodules
Let R be a commutative ring with identity and M be a unitary R-module. Let : S(M) −! S(M) [ {;} be a function, where S(M) is the set of submodules ofM. Suppose n 2 is a positive integer. A proper submodule P of M is called(n − 1, n) − -prime, if whenever a1, . . . , an−1 2 R and x 2 M and a1 . . . an−1x 2P(P), then there exists i 2 {1, . . . , n − 1} such that a1 . . . ai−1ai+1 . . . an−1x 2 P...
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ژورنال
عنوان ژورنال: Iraqi Journal of Science
سال: 2019
ISSN: 2312-1637,0067-2904
DOI: 10.24996/ijs.2019.60.11.17