Geodesic
Closure operators in modules and adjoint functors,~I
Algebra and discrete mathematics, Tome 25 (2018) no. 1, pp. 98-117

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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. 
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     author = {A. I. Kashu},
     title = {Closure operators in modules and adjoint {functors,~I}},
     journal = {Algebra and discrete mathematics},
     pages = {98--117},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2018_25_1_a7/}
}
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A. I. Kashu. Closure operators in modules and adjoint functors,~I. Algebra and discrete mathematics, Tome 25 (2018) no. 1, pp. 98-117. http://geodesic.mathdoc.fr/item/ADM_2018_25_1_a7/