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Morita contexts and closure operators in modules. (English) Zbl 1428.16005

Summary: The relations between the classes of closure operators of two module categories \(R\)-Mod and \(S\)-Mod are studied in the case when an arbitrary Morita context \(\,(R,_{ R}\,U_{ S},\, _{S}V_{R},S)\) is given. By the functors \(\mathrm{Hom}_{R}(U,\text{-})\) and \(\mathrm{Hom}_{S}(V,\text{-})\) two mappings are defined between the closure operators of these categories. Basic properties of these mappings are investigated.

MSC:

16D90 Module categories in associative algebras
16S90 Torsion theories; radicals on module categories (associative algebraic aspects)
06A15 Galois correspondences, closure operators (in relation to ordered sets)
16D10 General module theory in associative algebras
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References:

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