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Algebra Discrete Math., 2018, Volume 25, Issue 1, Pages 98–117 (Mi adm646)  

This article is cited in 1 scientific paper (total in 1 paper)

RESEARCH ARTICLE

Closure operators in modules and adjoint functors, I

A. I. Kashu

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

Abstract: In the present work the relations between the closure operators of two module categories are investigated in the case when the given categories are connected by two covariant adjoint functors $H\colon R-\operatorname{Mod}\longrightarrow S-\operatorname{Mod}$ and $T\colon S-\operatorname{Mod} \longrightarrow R-\operatorname{Mod}$. Two mappings are defined which ensure the transition between the closure operators of categories $R-\operatorname{Mod}$ and $S-\operatorname{Mod}$. Some important properties of these mappings are proved. It is shown that the studied mappings are compatible with the order relations and with the main operations.

Keywords: category of modules, closure operator, adjoint functors, lattice operations.

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MSC: 16D90, 16S90
Received: 07.07.2017
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Citation: A. I. Kashu, “Closure operators in modules and adjoint functors, I”, Algebra Discrete Math., 25:1 (2018), 98–117

Citation in format AMSBIB
\Bibitem{Kas18}
\by A.~I.~Kashu
\paper Closure operators in modules and adjoint functors,~I
\jour Algebra Discrete Math.
\yr 2018
\vol 25
\issue 1
\pages 98--117
\mathnet{http://mi.mathnet.ru/adm646}


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    This publication is cited in the following articles:
    1. A. I. Kashu, “Closure operators in modules and adjoint functors, II”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2018, no. 2, 101–112  mathnet
  • Algebra and Discrete Mathematics
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