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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

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

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
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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}