This article is cited 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.

MSC: 16D90, 16S90

Received: 07.07.2017

Language: English