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 quot...
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2016
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/admtest |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543345296277504 |
|---|---|
| author | Kashu, A. I. |
| author_facet | Kashu, A. I. |
| author_sort | Kashu, A. I. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2016-05-11T05:58:13Z |
| description | 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. |
| first_indexed | 2026-02-08T08:01:45Z |
| format | Article |
| id | admjournalluguniveduua-article-216 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T08:01:45Z |
| publishDate | 2016 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-2162016-05-11T05:58:13Z A survey of results on radicals and torsions in modules Kashu, A. I. ring, module, lattice, (pre\emph)radical, torsion, localization, 16D90, 16S90 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. Lugansk National Taras Shevchenko University 2016-05-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/admtest Algebra and Discrete Mathematics; Vol 21, No 1 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/admtest/pdf Copyright (c) 2016 Algebra and Discrete Mathematics |
| spellingShingle | ring module lattice (pre\emph)radical torsion localization, 16D90 16S90 Kashu, A. I. A survey of results on radicals and torsions in modules |
| title | A survey of results on radicals and torsions in modules |
| title_full | A survey of results on radicals and torsions in modules |
| title_fullStr | A survey of results on radicals and torsions in modules |
| title_full_unstemmed | A survey of results on radicals and torsions in modules |
| title_short | A survey of results on radicals and torsions in modules |
| title_sort | survey of results on radicals and torsions in modules |
| topic | ring module lattice (pre\emph)radical torsion localization, 16D90 16S90 |
| topic_facet | ring module lattice (pre\emph)radical torsion localization, 16D90 16S90 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/admtest |
| work_keys_str_mv | AT kashuai asurveyofresultsonradicalsandtorsionsinmodules AT kashuai surveyofresultsonradicalsandtorsionsinmodules |