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Algebra Discrete Math., 2013, Volume 16, Issue 1, Pages 81–95 (Mi adm436)  

This article is cited in 7 scientific papers (total in 7 papers)

RESEARCH ARTICLE

Closure operators in the categories of modules. Part II (Hereditary and cohereditary operators)

A. I. Kashu

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str., Chişinău, MD 2028 MOLDOVA

Abstract: This work is a continuation of the paper [1] (Part I), in which the weakly hereditary and idempotent closure operators of the category $R$-Mod are described. Using the results of [1], in this part the other classes of closure operators $C$ are characterized by the associated functions $\mathcal{F}_1^{C}$ and $\mathcal{F}_2^{C}$ which separate in every module $M \in R$-Mod the sets of $C$-dense submodules and $C$-closed submodules. This method is applied to the classes of hereditary, maximal, minimal and cohereditary closure operators.

Keywords: ring, module, preradical, closure operator, dense submodule, closed submodule, hereditary (cohereditary) closure operator.

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Bibliographic databases:
MSC: 16D90, 16S90, 06B23
Received: 03.06.2013
Revised: 03.06.2013
Language:

Citation: A. I. Kashu, “Closure operators in the categories of modules. Part II (Hereditary and cohereditary operators)”, Algebra Discrete Math., 16:1 (2013), 81–95

Citation in format AMSBIB
\Bibitem{Kas13}
\by A.~I.~Kashu
\paper Closure operators in the categories of modules. Part II (Hereditary and cohereditary operators)
\jour Algebra Discrete Math.
\yr 2013
\vol 16
\issue 1
\pages 81--95
\mathnet{http://mi.mathnet.ru/adm436}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3184700}


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    This publication is cited in the following articles:
    1. A. I. Kashu, “Closure operators in the categories of modules. Part III (Operations in $\mathbb{CO}$ and their properties)”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 1, 90–100  mathnet
    2. A. I. Kashu, “Preradicals, closure operators in $R$-Mod and connection between them”, Algebra Discrete Math., 18:1 (2014), 86–96  mathnet  mathscinet
    3. A. I. Kashu, “Closure operators in the categories of modules. Part IV (Relations between the operators and preradicals)”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 3, 13–22  mathnet
    4. A. I. Kashu, “A survey of results on radicals and torsions in modules”, Algebra Discrete Math., 21:1 (2016), 69–110  mathnet  mathscinet
    5. A. I. Kashu, “Pretorsions in modules and associated closure operators”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2017, no. 2, 24–41  mathnet  mathscinet
    6. A. I. Kashu, “Closure operators in modules and adjoint functors, I”, Algebra Discrete Math., 25:1 (2018), 98–117  mathnet
    7. A. I. Kashu, “Morita contexts and closure operators in modules”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2019, no. 1, 109–122  mathnet
  • Algebra and Discrete Mathematics
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