Biserial minor degenerations of matrix algebras over a field
Let n≥2 be a positive integer, K an arbitrary field, and q=[q⁽¹⁾|…|q⁽ⁿ⁾] an n-block matrix of n×n square matrices q⁽¹⁾,…,q⁽ⁿ⁾ with coefficients in K satisfying the conditions (C1) and (C2) listed in the introduction. We study minor degenerations Mqn(K) of the full matrix algebra Mn(K) in the sense o...
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| Дата: | 2010 |
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| Формат: | Стаття |
| Мова: | English |
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Інститут прикладної математики і механіки НАН України
2010
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| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/154533 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Biserial minor degenerations of matrix algebras over a field / A. Wlodarska // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 125–137. — Бібліогр.: 18 назв. — англ. |
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irk-123456789-1545332019-06-16T01:30:55Z Biserial minor degenerations of matrix algebras over a field Wlodarska, A. Let n≥2 be a positive integer, K an arbitrary field, and q=[q⁽¹⁾|…|q⁽ⁿ⁾] an n-block matrix of n×n square matrices q⁽¹⁾,…,q⁽ⁿ⁾ with coefficients in K satisfying the conditions (C1) and (C2) listed in the introduction. We study minor degenerations Mqn(K) of the full matrix algebra Mn(K) in the sense of Fujita-Sakai-Simson [7]. A characterisation of all block matrices q=[q⁽¹⁾|…|q⁽ⁿ⁾] such that the algebra Mqn(K) is basic and right biserial is given in the paper. We also prove that a basic algebra Mqn(K) is right biserial if and only if Mqn(K) is right special biserial. It is also shown that the K-dimensions of the left socle of Mqn(K) and of the right socle of Mqn(K) coincide, in case Mqn(K) is basic and biserial. 2010 Article Biserial minor degenerations of matrix algebras over a field / A. Wlodarska // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 125–137. — Бібліогр.: 18 назв. — англ. 1726-3255 2000 Mathematics Subject Classification:16G10, 16G60, 14R20, 16S80. http://dspace.nbuv.gov.ua/handle/123456789/154533 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Let n≥2 be a positive integer, K an arbitrary field, and q=[q⁽¹⁾|…|q⁽ⁿ⁾] an n-block matrix of n×n square matrices q⁽¹⁾,…,q⁽ⁿ⁾ with coefficients in K satisfying the conditions (C1) and (C2) listed in the introduction. We study minor degenerations Mqn(K) of the full matrix algebra Mn(K) in the sense of Fujita-Sakai-Simson [7]. A characterisation of all block matrices q=[q⁽¹⁾|…|q⁽ⁿ⁾] such that the algebra Mqn(K) is basic and right biserial is given in the paper. We also prove that a basic algebra Mqn(K) is right biserial if and only if Mqn(K) is right special biserial. It is also shown that the K-dimensions of the left socle of Mqn(K) and of the right socle of Mqn(K) coincide, in case Mqn(K) is basic and biserial. |
| format |
Article |
| author |
Wlodarska, A. |
| spellingShingle |
Wlodarska, A. Biserial minor degenerations of matrix algebras over a field Algebra and Discrete Mathematics |
| author_facet |
Wlodarska, A. |
| author_sort |
Wlodarska, A. |
| title |
Biserial minor degenerations of matrix algebras over a field |
| title_short |
Biserial minor degenerations of matrix algebras over a field |
| title_full |
Biserial minor degenerations of matrix algebras over a field |
| title_fullStr |
Biserial minor degenerations of matrix algebras over a field |
| title_full_unstemmed |
Biserial minor degenerations of matrix algebras over a field |
| title_sort |
biserial minor degenerations of matrix algebras over a field |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/154533 |
| citation_txt |
Biserial minor degenerations of matrix algebras over a field / A. Wlodarska // Algebra and Discrete Mathematics. — 2010. — Vol. 9, № 2. — С. 125–137. — Бібліогр.: 18 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
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2023-05-20T17:44:54Z |
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