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Algebra and Discrete Mathematics, 2018, Volume 25, Issue 1, Pages 98–117
(Mi adm646)
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This article is cited in 2 scientific papers (total in 2 papers)
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 $H\colon R\text{-}\operatorname{Mod}\longrightarrow S\text{-}\operatorname{Mod}$ and $T\colon S\text{-}\operatorname{Mod} \longrightarrow R\text{-}\operatorname{Mod}$. Two mappings are defined which ensure the transition between the closure operators of categories $R\text{-}\operatorname{Mod}$ and $S\text{-}\operatorname{Mod}$. 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.
Received: 07.07.2017
Citation:
A. I. Kashu, “Closure operators in modules and adjoint functors, I”, Algebra Discrete Math., 25:1 (2018), 98–117
Linking options:
https://www.mathnet.ru/eng/adm646 https://www.mathnet.ru/eng/adm/v25/i1/p98
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Abstract page: | 158 | Full-text PDF : | 34 | References: | 22 |
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