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Algebra Discrete Math., 2016, Volume 21, Issue 1, Pages 69–110 (Mi adm555)  

SURVEY ARTICLE

A survey of results on radicals and torsions in modules

A. I. Kashu

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, 5 Academiei str., Chişinău, MD 2028 MOLDOVA

Abstract: 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.

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

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Bibliographic databases:

Document Type: Article
MSC: 16D90, 16S90
Received: 18.12.2015
Language: English

Citation: A. I. Kashu, “A survey of results on radicals and torsions in modules”, Algebra Discrete Math., 21:1 (2016), 69–110

Citation in format AMSBIB
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\by A.~I.~Kashu
\paper A survey of results on radicals and torsions in modules
\jour Algebra Discrete Math.
\yr 2016
\vol 21
\issue 1
\pages 69--110
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3537486}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000382847600007}


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