## 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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