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Algebra and Discrete Mathematics, 2013, Volume 15, Issue 2, Pages 213–228
(Mi adm422)
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This article is cited in 9 scientific papers (total in 9 papers)
RESEARCH ARTICLE
Closure operators in the categories of modules. Part I (Weakly hereditary and idempotent operators)
A. I. Kashu Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str., Chişinău,
MD – 2028 MOLDOVA
Abstract:
In this work the closure operators of a category of modules $R$-Mod are studied. Every closure operator $C$ of $R$-Mod defines two functions $\mathcal{F}_1^{C}$ and $\mathcal{F}_2^{C}$, which in every module $M$ distinguish the set of $C$-dense submodules $\mathcal{F}_1^{C}(M)$ and the set of $C$-closed submodules $\mathcal{F}_2^{C}(M)$. By means of these functions three types of closure operators are described: 1) weakly hereditary; 2) idempotent; 3) weakly hereditary and idempotent.
Keywords:
ring, module, lattice, preradical, closure operator, lattice of submodules, dense submodule, closed submodule.
Received: 19.02.2013 Revised: 25.05.2013
Citation:
A. I. Kashu, “Closure operators in the categories of modules. Part I (Weakly hereditary and idempotent operators)”, Algebra Discrete Math., 15:2 (2013), 213–228
Linking options:
https://www.mathnet.ru/eng/adm422 https://www.mathnet.ru/eng/adm/v15/i2/p213
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Abstract page: | 306 | Full-text PDF : | 173 | References: | 58 |
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