Jordan regular units in rings and group rings
UDC 512.5 The concept of Lie regular elements and Lie regular units was defined and studied by Kanwar, Sharma and Yadav in Lie regular generators of general linear groups, Comm. Algebra, 40, № 4, 1304–1315 (2012)]. We introduce Jordan regular elements and Jordan regular units.&n...
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| Дата: | 2023 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2023
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/1130 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860507148631408640 |
|---|---|
| author | Kumari, P. Sahai, M. Sharma, R. K. Kumari, P. Sahai, M. Sharma, R. K. |
| author_facet | Kumari, P. Sahai, M. Sharma, R. K. Kumari, P. Sahai, M. Sharma, R. K. |
| author_sort | Kumari, P. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2023-04-15T15:10:29Z |
| description | UDC 512.5
The concept of Lie regular elements and Lie regular units was defined and studied by Kanwar, Sharma and Yadav in Lie regular generators of general linear groups, Comm. Algebra, 40, № 4, 1304–1315 (2012)]. We introduce Jordan regular elements and Jordan regular units. It is proved that the order of the set of Jordan regular units in $M(2, Z_{2^n})$ is equal to a half of the order of $U(M(2,Z_{2^n})).$ Further, we show that the group ring $KG$ of a group $G$ over a field $K$ of characteristic $2$ has no Jordan regular units. |
| doi_str_mv | 10.37863/umzh.v75i3.1130 |
| first_indexed | 2026-03-24T02:04:43Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-1130 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T02:04:43Z |
| publishDate | 2023 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-11302023-04-15T15:10:29Z Jordan regular units in rings and group rings Jordan regular units in rings and group rings Kumari, P. Sahai, M. Sharma, R. K. Kumari, P. Sahai, M. Sharma, R. K. JORDAN REGULAR UNITS UDC 512.5 The concept of Lie regular elements and Lie regular units was defined and studied by Kanwar, Sharma and Yadav in Lie regular generators of general linear groups, Comm. Algebra, 40, № 4, 1304–1315 (2012)]. We introduce Jordan regular elements and Jordan regular units. It is proved that the order of the set of Jordan regular units in $M(2, Z_{2^n})$ is equal to a half of the order of $U(M(2,Z_{2^n})).$ Further, we show that the group ring $KG$ of a group $G$ over a field $K$ of characteristic $2$ has no Jordan regular units. УДК 512.5 Регулярні одиниці Жордана в кільцях і групових кільцях Поняття регулярних елементів Лі та регулярних одиниць Лі було введено та вивчено Канваром, Шармою та Ядавом у Lie regular generators of general linear groups, Comm. Algebra, 40, № 4, 1304–1315 (2012)]. Ми вводимо регулярні елементи Жордана та регулярні одиниці Жордана. Доведено, що порядок множини регулярних одиниць Жордана в $M(2, Z_{2^n})$ становить половину порядку $U(M(2,Z_{2^n})).$  Крім того,  показано, що  групове кільце $KG$ групи $G$ над полем $K$ характеристики $2$ не має регулярних одиниць Жордана.  Institute of Mathematics, NAS of Ukraine 2023-04-11 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/1130 10.37863/umzh.v75i3.1130 Ukrains’kyi Matematychnyi Zhurnal; Vol. 75 No. 3 (2023); 351 - 363 Український математичний журнал; Том 75 № 3 (2023); 351 - 363 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/1130/9790 Copyright (c) 2023 Parvesh Kumari, Meena Sahai, R. K. Sharma |
| spellingShingle | Kumari, P. Sahai, M. Sharma, R. K. Kumari, P. Sahai, M. Sharma, R. K. Jordan regular units in rings and group rings |
| title | Jordan regular units in rings and group rings |
| title_alt | Jordan regular units in rings and group rings |
| title_full | Jordan regular units in rings and group rings |
| title_fullStr | Jordan regular units in rings and group rings |
| title_full_unstemmed | Jordan regular units in rings and group rings |
| title_short | Jordan regular units in rings and group rings |
| title_sort | jordan regular units in rings and group rings |
| topic_facet | JORDAN REGULAR UNITS |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/1130 |
| work_keys_str_mv | AT kumarip jordanregularunitsinringsandgrouprings AT sahaim jordanregularunitsinringsandgrouprings AT sharmark jordanregularunitsinringsandgrouprings AT kumarip jordanregularunitsinringsandgrouprings AT sahaim jordanregularunitsinringsandgrouprings AT sharmark jordanregularunitsinringsandgrouprings |