On elementarity of radical classes of modules over noncommutative dedekind duo-domains
We find some sufficient conditions for a radical class of an idempotent radical in the category of modules over a Dedekind left bounded duo-domain to be axiomatizable. In the case of the integer numbers ring this result implies the Gorbachuk-Komarnitskii Theorem on axiomatizable radical classes of A...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vasyl Stefanyk Precarpathian National University
2012-12-01
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| Series: | Karpatsʹkì Matematičnì Publìkacìï |
| Subjects: | |
| Online Access: | https://journals.pnu.edu.ua/index.php/cmp/article/view/2148 |
| _version_ | 1819074936664227840 |
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| author | Y.T Bilyak M.Ya Komarnitskii |
| author_facet | Y.T Bilyak M.Ya Komarnitskii |
| author_sort | Y.T Bilyak |
| collection | DOAJ |
| description | We find some sufficient conditions for a radical class of an idempotent radical in the category of modules over a Dedekind left bounded duo-domain to be axiomatizable. In the case of the integer numbers ring this result implies the Gorbachuk-Komarnitskii Theorem on axiomatizable radical classes of Abelian groups. |
| first_indexed | 2024-12-21T18:17:26Z |
| format | Article |
| id | doaj.art-6bdd3b23a2b94a1594fe22f0a5fd723d |
| institution | Directory Open Access Journal |
| issn | 2075-9827 2313-0210 |
| language | English |
| last_indexed | 2024-12-21T18:17:26Z |
| publishDate | 2012-12-01 |
| publisher | Vasyl Stefanyk Precarpathian National University |
| record_format | Article |
| series | Karpatsʹkì Matematičnì Publìkacìï |
| spelling | doaj.art-6bdd3b23a2b94a1594fe22f0a5fd723d2022-12-21T18:54:38ZengVasyl Stefanyk Precarpathian National UniversityKarpatsʹkì Matematičnì Publìkacìï2075-98272313-02102012-12-01421972032148On elementarity of radical classes of modules over noncommutative dedekind duo-domainsY.T Bilyak0M.Ya Komarnitskii1Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, UkraineIvan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, UkraineWe find some sufficient conditions for a radical class of an idempotent radical in the category of modules over a Dedekind left bounded duo-domain to be axiomatizable. In the case of the integer numbers ring this result implies the Gorbachuk-Komarnitskii Theorem on axiomatizable radical classes of Abelian groups.https://journals.pnu.edu.ua/index.php/cmp/article/view/2148noncommutative dedekind domainduo-domainradicalultraproduct |
| spellingShingle | Y.T Bilyak M.Ya Komarnitskii On elementarity of radical classes of modules over noncommutative dedekind duo-domains Karpatsʹkì Matematičnì Publìkacìï noncommutative dedekind domain duo-domain radical ultraproduct |
| title | On elementarity of radical classes of modules over noncommutative dedekind duo-domains |
| title_full | On elementarity of radical classes of modules over noncommutative dedekind duo-domains |
| title_fullStr | On elementarity of radical classes of modules over noncommutative dedekind duo-domains |
| title_full_unstemmed | On elementarity of radical classes of modules over noncommutative dedekind duo-domains |
| title_short | On elementarity of radical classes of modules over noncommutative dedekind duo-domains |
| title_sort | on elementarity of radical classes of modules over noncommutative dedekind duo domains |
| topic | noncommutative dedekind domain duo-domain radical ultraproduct |
| url | https://journals.pnu.edu.ua/index.php/cmp/article/view/2148 |
| work_keys_str_mv | AT ytbilyak onelementarityofradicalclassesofmodulesovernoncommutativededekindduodomains AT myakomarnitskii onelementarityofradicalclassesofmodulesovernoncommutativededekindduodomains |