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**Adjoint functors, preradicals and closure operators in module categories.**
*(English)*
Zbl 1453.16008

Summary: In this article preradicals and closure operators are studied in an adjoint situation, defined by two covariant functors between the module categories \(R\)-Mod and \(S\)-Mod. The mappings which determine the relationship between the classes of preradicals and the classes of closure operators of these categories are investigated. The goal of research is to elucidate the concordance (compatibility) of these mappings. For that some combinations of them, consisting of four mappings, are considered and the commutativity of corresponding diagrams (squares) is studied. The obtained results show the connection between considered mappings in adjoint situation.

### MSC:

16D90 | Module categories in associative algebras |

16S90 | Torsion theories; radicals on module categories (associative algebraic aspects) |

18A40 | Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.) |

18E40 | Torsion theories, radicals |

06A15 | Galois correspondences, closure operators (in relation to ordered sets) |

### Keywords:

closure operator; adjoint functors; preradical; category of modules; natural transformation; lattice of submodules
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\textit{A. I. Kashu}, Algebra Discrete Math. 28, No. 2, 260--277 (2019; Zbl 1453.16008)

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### References:

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