Results 171 to 180 of about 22,762 (212)
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T-SMALL SUBMODULES WITH RESPECT TO AN ARBITRARY SUBMODULE
JP Journal of Algebra, Number Theory and Applications, 2018Summary: From the notion of small submodules, for submodules \(T\) and \(M'\) of an \(R\)-module \(M\), we define \(T\)-small submodules with respect to a submodule \(M'\) of a module \(M\), where \(T\cap M'\neq 0\). We show that \(T\)-small submodules with respect to \(M'\) are a generalization of small submodules.
Sangwirotjanapat, Sukit +1 more
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Large-maximal small submodules
Journal of Interdisciplinary Mathematics, 2023In this study, the ideas of Large-maximal small submodules and Large-maximal small radical of modules are presented. The primary attributes and features of the concept of large-maximal small submodules are provided. Additionally, we discuss the connections between this idea and various submodule kinds with the help of examples and observations that are
Wafaa H. Hanoon, Atwar A. Abboodi
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Modules with finitely many small submodules
Asian-European Journal of Mathematics, 2022O. A. S. Karamzadeh et al. [On rings with a unique proper essential right ideal, Fund. Math. 183 (2004) 229–244] introduced a class of modules with unique proper essential submodule, such modules are called as ue-modules. A. Azarang and F. Shahrisvand [Rings with only finitely many essential right ideals, Comm.
Avanish Kumar Chaturvedi, Nirbhay Kumar
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2022
Let $R$ be a commutative ring with identity, and (U_{R}) be an $R$-module, with (E = End(U_{R})). In this work we consider a generalization of class small essential submodules namely E-small essential submodules. Where the submodule $Q$ of (U_{R}) is said E-small essential if $Q$ (cap W = 0) , when W is a small submodule of (U_{R}), implies that (N_{S ...
Khalf, Mamoon, Abbas, Hind
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Let $R$ be a commutative ring with identity, and (U_{R}) be an $R$-module, with (E = End(U_{R})). In this work we consider a generalization of class small essential submodules namely E-small essential submodules. Where the submodule $Q$ of (U_{R}) is said E-small essential if $Q$ (cap W = 0) , when W is a small submodule of (U_{R}), implies that (N_{S ...
Khalf, Mamoon, Abbas, Hind
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Dimension of Non-small Submodules
Bulletin of the Iranian Mathematical Society, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the small intersection graph of submodules of a module
2021Summary: Let \(M\) be a unitary left \(R\)-module, where \(R\) is a (not necessarily commutative) ring with identity. The small intersection graph of nontrivial submodules of \(M\), denoted by \(\Gamma(M)\), is an undirected simple graph whose vertices are in one-to-one correspondence with all nontrivial submodules of \(M\) and two distinct vertices ...
Mahdavi, Lotf Ali, Talebi, Yahya
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Hopfcity and Jacobson small submodules
2023In this paper, the author generalizing the notions of generalized Hopfian module, weakly Hopfian module, \(\delta\)-weakly Hopfian module, defines a Jacobson weakly Hopfian module (which we write, in short, in this review, as \(J\)-\(w\) Hopfian module) and investigates its properties. The author derives equivalent conditions for a projective module to
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2020
In this work, every ring have unity and every module is unital left module. Let M be an R-module and N < M. If N < RadM, then N is called a radical small (or briefly r-small) submodule of M and denoted by N
NEBİYEV, Celil, ÖKTEN, Hasan Hüseyin
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In this work, every ring have unity and every module is unital left module. Let M be an R-module and N < M. If N < RadM, then N is called a radical small (or briefly r-small) submodule of M and denoted by N
NEBİYEV, Celil, ÖKTEN, Hasan Hüseyin
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Almost small semiprime submodules
Journal of Discrete Mathematical Sciences and Cryptography, 2021Haider A. Ramadhan, Nuhad S. Al-Mothafar
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