Adjoint functors, preradicals and closure operators in module categories
In this article preradicals and closure operators are studied in an adjoint situation, defined by two covariant functors between the module categories \(R\)-Mod and \(S\)-Mod. The mappings which determine the relationship between the classes of preradicals and the classes of closure operators of the...
Gespeichert in:
| Datum: | 2020 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2020
|
| Schlagworte: | |
| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1322 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| _version_ | 1856543420400533504 |
|---|---|
| author | Kashu, Alexei I. |
| author_facet | Kashu, Alexei I. |
| author_sort | Kashu, Alexei I. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2020-02-10T19:12:26Z |
| description | In this article preradicals and closure operators are studied in an adjoint situation, defined by two covariant functors between the module categories \(R\)-Mod and \(S\)-Mod. The mappings which determine the relationship between the classes of preradicals and the classes of closure operators of these categories are investigated. The goal of research is to elucidate the concordance (compatibility) of these mappings. For that some combinations of them, consisting of four mappings, are considered and the commutativity of corresponding diagrams (squares) is studied. The obtained results show the connection between considered mappings in adjoint situation. |
| first_indexed | 2025-12-02T15:42:05Z |
| format | Article |
| id | admjournalluguniveduua-article-1322 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:42:05Z |
| publishDate | 2020 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-13222020-02-10T19:12:26Z Adjoint functors, preradicals and closure operators in module categories Kashu, Alexei I. closure operator, adjoint functors, preradical, category of modules, natural transformation, lattice of submodules 16D90, 16S90, 18A40, 18E40, 06A15 In this article preradicals and closure operators are studied in an adjoint situation, defined by two covariant functors between the module categories \(R\)-Mod and \(S\)-Mod. The mappings which determine the relationship between the classes of preradicals and the classes of closure operators of these categories are investigated. The goal of research is to elucidate the concordance (compatibility) of these mappings. For that some combinations of them, consisting of four mappings, are considered and the commutativity of corresponding diagrams (squares) is studied. The obtained results show the connection between considered mappings in adjoint situation. Lugansk National Taras Shevchenko University 2020-02-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1322 Algebra and Discrete Mathematics; Vol 28, No 2 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1322/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1322/493 Copyright (c) 2020 Algebra and Discrete Mathematics |
| spellingShingle | closure operator adjoint functors preradical category of modules natural transformation lattice of submodules 16D90 16S90 18A40 18E40 06A15 Kashu, Alexei I. Adjoint functors, preradicals and closure operators in module categories |
| title | Adjoint functors, preradicals and closure operators in module categories |
| title_full | Adjoint functors, preradicals and closure operators in module categories |
| title_fullStr | Adjoint functors, preradicals and closure operators in module categories |
| title_full_unstemmed | Adjoint functors, preradicals and closure operators in module categories |
| title_short | Adjoint functors, preradicals and closure operators in module categories |
| title_sort | adjoint functors, preradicals and closure operators in module categories |
| topic | closure operator adjoint functors preradical category of modules natural transformation lattice of submodules 16D90 16S90 18A40 18E40 06A15 |
| topic_facet | closure operator adjoint functors preradical category of modules natural transformation lattice of submodules 16D90 16S90 18A40 18E40 06A15 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1322 |
| work_keys_str_mv | AT kashualexeii adjointfunctorspreradicalsandclosureoperatorsinmodulecategories |