A survey of results on radicals and torsions in modules
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...
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| Date: | 2016 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2016
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| Series: | Algebra and Discrete Mathematics |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | A survey of results on radicals and torsions in modules / A.I. Kashu // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 1. — С. 69-110. — Бібліогр.: 66 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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. |
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