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Algebra and Discrete Mathematics, 2016, том 21, выпуск 1, страницы 69–110
(Mi adm555)
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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
Аннотация:
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.
Ключевые слова:
ring, module, lattice, (pre)radical, torsion, localization, adjoint functor, Morita context, closure operator.
Поступила в редакцию: 18.12.2015
Образец цитирования:
A. I. Kashu, “A survey of results on radicals and torsions in modules”, Algebra Discrete Math., 21:1 (2016), 69–110
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm555 https://www.mathnet.ru/rus/adm/v21/i1/p69
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Страница аннотации: | 234 | PDF полного текста: | 110 | Список литературы: | 41 |
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