Criteria for Invertibility of Elements in Associates
We continue the investigation of invertible elements in associates, i.e., in (n + 1)-ary groupoids that are (i, j)-associative for all i ≡ j (mod s), where s is a divisor of a number n. For s = 1, an arbitrary associate is a semigroup. We establish two new criteria for the invertibility of elements,...
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| Datum: | 2001 |
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| Hauptverfasser: | , |
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| Sprache: | Ukrainisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2001
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/4375 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510504640839680 |
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| author | Yurevych, О. V. Юревич, О. В. |
| author_facet | Yurevych, О. V. Юревич, О. В. |
| author_sort | Yurevych, О. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:27:24Z |
| description | We continue the investigation of invertible elements in associates, i.e., in (n + 1)-ary groupoids that are (i, j)-associative for all i ≡ j (mod s), where s is a divisor of a number n. For s = 1, an arbitrary associate is a semigroup. We establish two new criteria for the invertibility of elements, which generalize the results obtained earlier, and formulate corollaries for (n + 1)-groups and polyagroups, i.e., quasigroup associates. |
| first_indexed | 2026-03-24T02:58:03Z |
| format | Article |
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| id | umjimathkievua-article-4375 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:58:03Z |
| publishDate | 2001 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/98/85f41fc29bf0f158a3c6a8059edf2f98.pdf |
| spelling | umjimathkievua-article-43752020-03-18T20:27:24Z Criteria for Invertibility of Elements in Associates Критерії оборотності елементів в асоціатах Yurevych, О. V. Юревич, О. В. We continue the investigation of invertible elements in associates, i.e., in (n + 1)-ary groupoids that are (i, j)-associative for all i ≡ j (mod s), where s is a divisor of a number n. For s = 1, an arbitrary associate is a semigroup. We establish two new criteria for the invertibility of elements, which generalize the results obtained earlier, and formulate corollaries for (n + 1)-groups and polyagroups, i.e., quasigroup associates. Продовжується вивчення оборотних елементів в асоціатах, тобто в $(n + 1)$-арних групоїдах, які є $(і, j)$-асоціативними для всіх $і = j (\mod s)$, де $s$— дільник числа $n$. При $s = 1$ довільний асоціат є напівгрупою. Встановлено два нових критерії оборотності елементів, чим узагальнено раніше одержані результати, наведено наслідки для $(n + 1)$-груп і поліагруп, тобто квазігрупових асоціатів. Institute of Mathematics, NAS of Ukraine 2001-11-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4375 Ukrains’kyi Matematychnyi Zhurnal; Vol. 53 No. 11 (2001); 1556-1563 Український математичний журнал; Том 53 № 11 (2001); 1556-1563 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4375/5454 https://umj.imath.kiev.ua/index.php/umj/article/view/4375/5455 Copyright (c) 2001 Yurevych О. V. |
| spellingShingle | Yurevych, О. V. Юревич, О. В. Criteria for Invertibility of Elements in Associates |
| title | Criteria for Invertibility of Elements in Associates |
| title_alt | Критерії оборотності елементів в асоціатах |
| title_full | Criteria for Invertibility of Elements in Associates |
| title_fullStr | Criteria for Invertibility of Elements in Associates |
| title_full_unstemmed | Criteria for Invertibility of Elements in Associates |
| title_short | Criteria for Invertibility of Elements in Associates |
| title_sort | criteria for invertibility of elements in associates |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4375 |
| work_keys_str_mv | AT yurevychov criteriaforinvertibilityofelementsinassociates AT ûrevičov criteriaforinvertibilityofelementsinassociates AT yurevychov kriterííoborotnostíelementívvasocíatah AT ûrevičov kriterííoborotnostíelementívvasocíatah |