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On L-Fuzzy Multiplication Modules
Discussiones Mathematicae - General Algebra and Applications, 2017 Let L be a complete lattice. In a manner analogous to a commutative ring, we introduce and investigate the L-fuzzy multiplication modules over a commutative ring with non-zero identity.
Atani Shahabaddin Ebrahimi +1 more
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On the prime submodules of multiplication modules [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 By considering the notion of multiplication modules over a commutative ring with identity, first we introduce the notion product of two submodules of such modules. Then we use this notion to characterize the prime submodules of a multiplication module.
Reza Ameri
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Prime, weakly prime and almost prime elements in multiplication lattice modules
Open Mathematics, 2016 In this paper, we study multiplication lattice modules. We establish a new multiplication over elements of a multiplication lattice module.With this multiplication, we characterize idempotent element, prime element, weakly prime element and almost prime ...
Emel Aslankarayiğit Ugurlu +1 more
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On multiplication $fs$-modules and dimension symmetry [PDF]
Journal of Mahani Mathematical Research, 2023 In this paper, we first study $fs$-modules, i.e., modules with finitely many small submodules. We show that every $fs$-module with finite hollow dimension is Noetherian.
Nasrin Shirali +2 more
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Canadian Mathematical Bulletin, 1979 All rings R considered here are commutative with identity and all the modules are unital right modules. As defined by Mehdi [6] a module MR is said to be a multiplication module if for every pair of submodules K and N of M, K ⊂ N implies K=NA for some ideal A of R. This concept generalizes the well known concept of a multiplication ring.
Singh, Surjeet, Mehdi, Fazal
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MULTIPLICATION MODULES THAT ARE FINITELY GENERATED [PDF]
Journal of Algebraic Systems, 2020 Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module. An $R$-module $M$ is called a multiplication module if for every submodule $N$ of $M$ there exists an ideal $I$ of $R$ such that $N = IM$.
Y. Tolooei
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SUBMODULES OF MULTIPLICATION MODULES
Taiwanese Journal of Mathematics, 2005 Let \(R\) be a commutative ring with identity and \(M\) an (unitary) \(R\)-module. We say that \(M\) is multiplication module if for each submodule \(N\) of \(M,N = IM\) for some ideal \(I\) of \(R\). In this paper, the author studies the set \(S(M)\) of finitely generated faithful multiplication submodules of a finitely generated faithful ...
Shahabaddin Ebrahimi Atani
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ON COMULTIPLICATION AND R-MULTIPLICATION MODULES [PDF]
Journal of Algebraic Systems, 2014 We state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings.
Ashkan Nikseresht, Habib Sharif
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IDEALS AND SUBMODULES OF MULTIPLICATION MODULES [PDF]
Journal of the Korean Mathematical Society, 2005 Let \(R\) be commutative ring with the unity and the modules are unitary. For an \(R\)-module \(M\) the following sets of prime ideals \(P\in \text{Spec}(R)\) are of interest: \(N(M)=\{P: PM\neq M\}\), \(V(\text{ann}_R(M))=\{P:\text{ann}_R(M)\subseteq P\}\), \(\text{Supp}(M)=\{P:M_P\neq 0\}\), where \(\text{ann}_R(M)=\{r\in R:rM=0 \}\) is the ...
Lee, Sang Cheol +2 more
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Characterizations of Weakly Approximately Primary Submodules in Some Types of Modules
Tikrit Journal of Pure Science, 2021 Our aim in this note is to introduce several characterizations of weakly approximately primary submodules in class of multiplication modules. Furthermore, we characterized weakly approximately primary submodules by theirs resudule in the class of ...
Khaled Y. Jhad, Bothaynah N. Shahab
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