A survey of results on radicals and torsions in modules

A. I. Kashu

Algebra and discrete mathematics, Tome 21 (2016) no. 1, pp. 69-110.

Résumé

In this work basic results of the author on radicals in module categories are presented in a short form. Principal topics are: types of preradicals and their characterizations; classes of $R$-modules and sets of left ideals of $ R$; notions and constructions associated to radicals; rings of quotients and localizations; preradicals in adjoint situation; torsions in Morita contexts; duality between localizations and colocalizations; principal functors and preradicals; special classes of modules; preradicals and operations in the lattices of submodules; closure operators and preradicals.

Détail

Keywords: ring, lattice, (pre)radical, localization, adjoint functor, closure operator.
Mots-clés : module, torsion, Morita context

Bibliographie

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[60] Kashu A. I., “On inverse operations in the lattices of submodules”, Algebra and Discrete Mathematics, 13:2 (2012), 273–288 | MR | Zbl

[61] Kashu A. I., “On partial inverse operations in the lattice of submodules”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2012, no. 2(69), 59–73 | MR | Zbl

[62] Kashu A. I., “Closure operators in the categories of modules. Part I”, Algebra and Discrete Mathematics, 15:2 (2013), 213–228 | MR | Zbl

[63] Kashu A. I., “Closure operators in the categories of modules. Part II”, Algebra and Discrete Mathematics, 16:1 (2013), 81–95 | MR | Zbl

[64] Kashu A. I., “Closure operators in the categories of modules. Part III”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2014, no. 1(74), 90–100 | MR | Zbl

[65] Kashu A. I., “Preradicals, closure operators in $R$-$\mathrm{Mod}$ and connection between them”, Algebra and Discrete Mathematics, 18:1 (2014), 87–97 | MR

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