A note on the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$
UDC 512.5 The dimension of the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$ and the algebraic structure of $\dfrac{\mathbb F_{2^n} D_{{2^{k}} {3}}} {J(\mathbb F_{2^n}D_{2^{k} {3}})}$ are determined. Here, $D_{2m}$ represents the dihedral group of order $2m,$ $\mathbb F_{2^n}$ represents any finite fi...
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| Date: | 2024 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Institute of Mathematics, NAS of Ukraine
2024
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7623 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512689472667648 |
|---|---|
| author | Kumar, Yogesh Sharma, R. K. Kumar, Yogesh Sharma, R. K. |
| author_facet | Kumar, Yogesh Sharma, R. K. Kumar, Yogesh Sharma, R. K. |
| author_sort | Kumar, Yogesh |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-02-11T07:16:09Z |
| description | UDC 512.5
The dimension of the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$ and the algebraic structure of $\dfrac{\mathbb F_{2^n} D_{{2^{k}} {3}}} {J(\mathbb F_{2^n}D_{2^{k} {3}})}$ are determined. Here, $D_{2m}$ represents the dihedral group of order $2m,$ $\mathbb F_{2^n}$ represents any finite field of characteristic $2$, and $F_{2^n}D_{2m}$ represents the group algebra of the group $D_{2m}$ over the field $\mathbb F_{2^n}.$ |
| doi_str_mv | 10.3842/umzh.v76i8.7623 |
| first_indexed | 2026-03-24T03:32:47Z |
| format | Article |
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| id | umjimathkievua-article-7623 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:32:47Z |
| publishDate | 2024 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-76232025-02-11T07:16:09Z A note on the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$ A note on the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$ Kumar, Yogesh Sharma, R. K. Kumar, Yogesh Sharma, R. K. Group algebra, Jacobson Radical, Unit Group. UDC 512.5 The dimension of the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$ and the algebraic structure of $\dfrac{\mathbb F_{2^n} D_{{2^{k}} {3}}} {J(\mathbb F_{2^n}D_{2^{k} {3}})}$ are determined. Here, $D_{2m}$ represents the dihedral group of order $2m,$ $\mathbb F_{2^n}$ represents any finite field of characteristic $2$, and $F_{2^n}D_{2m}$ represents the group algebra of the group $D_{2m}$ over the field $\mathbb F_{2^n}.$ УДК 512.5 Примітка щодо радикала Джекобсона $J(\mathbb F_{2^n}D_{2m})$ Визначено розмірність радикала Джекобсона $J(\mathbb F_{2^n}D_{2m})$ та алгебраїчну структуру  $\dfrac{\mathbb F_{2^n}D_{2^k3}}{J( \mathbb F_{2^n}D_{2^k3})}.$ Тут $D_{2m}$ – діедрична група порядку $2m$, $\mathbb F_{2^n}$  –  будь-яке скінченне поле з характеристикою $2$, а $F_{2^n}D_{2m} $  –  групова алгебра групи $D_{2m}$ над полем $\mathbb F_{2^n}.$ Institute of Mathematics, NAS of Ukraine 2024-09-04 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7623 10.3842/umzh.v76i8.7623 Ukrains’kyi Matematychnyi Zhurnal; Vol. 76 No. 8 (2024); 1265 - 1268 Український математичний журнал; Том 76 № 8 (2024); 1265 - 1268 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7623/10161 Copyright (c) 2024 Yogesh Kumar Yogesh Kumar |
| spellingShingle | Kumar, Yogesh Sharma, R. K. Kumar, Yogesh Sharma, R. K. A note on the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$ |
| title | A note on the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$ |
| title_alt | A note on the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$ |
| title_full | A note on the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$ |
| title_fullStr | A note on the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$ |
| title_full_unstemmed | A note on the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$ |
| title_short | A note on the Jacobson radical $J(\mathbb F_{2^n}D_{2m})$ |
| title_sort | note on the jacobson radical $j(\mathbb f_{2^n}d_{2m})$ |
| topic_facet | Group algebra Jacobson Radical Unit Group. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7623 |
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