Lattices of classes of groupoids with one-sided quasigroup conditions
It is shown that two classes of groupoids satisfying certain one-sided quasigroup conditions, namely the classes of one-sided torsion groupoids and of one-sided finite exponent groupoids, are complete lattices, both isomorphic to the lattice of Steinitz numbers with the divisibility relation.
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| Date: | 2018 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2018
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/620 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543156018872320 |
|---|---|
| author | Galuszka, Jan |
| author_facet | Galuszka, Jan |
| author_sort | Galuszka, Jan |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T08:18:32Z |
| description | It is shown that two classes of groupoids satisfying certain one-sided quasigroup conditions, namely the classes of one-sided torsion groupoids and of one-sided finite exponent groupoids, are complete lattices, both isomorphic to the lattice of Steinitz numbers with the divisibility relation. |
| first_indexed | 2026-02-08T07:58:44Z |
| format | Article |
| id | admjournalluguniveduua-article-620 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:58:44Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-6202018-04-04T08:18:32Z Lattices of classes of groupoids with one-sided quasigroup conditions Galuszka, Jan Groupoid, quasigroup, right quasigroup, left quasigroup, Steinitz numbers 05B15, 08A30, 08A40, 08A62, 08A99, 14R10, 20N02, 20N05 It is shown that two classes of groupoids satisfying certain one-sided quasigroup conditions, namely the classes of one-sided torsion groupoids and of one-sided finite exponent groupoids, are complete lattices, both isomorphic to the lattice of Steinitz numbers with the divisibility relation. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/620 Algebra and Discrete Mathematics; Vol 9, No 1 (2010) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/620/155 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Groupoid quasigroup right quasigroup left quasigroup Steinitz numbers 05B15 08A30 08A40 08A62 08A99 14R10 20N02 20N05 Galuszka, Jan Lattices of classes of groupoids with one-sided quasigroup conditions |
| title | Lattices of classes of groupoids with one-sided quasigroup conditions |
| title_full | Lattices of classes of groupoids with one-sided quasigroup conditions |
| title_fullStr | Lattices of classes of groupoids with one-sided quasigroup conditions |
| title_full_unstemmed | Lattices of classes of groupoids with one-sided quasigroup conditions |
| title_short | Lattices of classes of groupoids with one-sided quasigroup conditions |
| title_sort | lattices of classes of groupoids with one-sided quasigroup conditions |
| topic | Groupoid quasigroup right quasigroup left quasigroup Steinitz numbers 05B15 08A30 08A40 08A62 08A99 14R10 20N02 20N05 |
| topic_facet | Groupoid quasigroup right quasigroup left quasigroup Steinitz numbers 05B15 08A30 08A40 08A62 08A99 14R10 20N02 20N05 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/620 |
| work_keys_str_mv | AT galuszkajan latticesofclassesofgroupoidswithonesidedquasigroupconditions |