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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2010 |
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| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2010
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/154533 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862735291918319616 |
|---|---|
| author | Wlodarska, A. |
| author_facet | Wlodarska, A. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T19:47:50Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-154533 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:47:50Z |
| publishDate | 2010 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Wlodarska, A. 2019-06-15T16:27:34Z 2019-06-15T16:27:34Z 2010 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. https://nasplib.isofts.kiev.ua/handle/123456789/154533 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. An author is supported by Polish Research Grant N N201/2692/35/2008-2011. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Biserial minor degenerations of matrix algebras over a field Article published earlier |
| spellingShingle | Biserial minor degenerations of matrix algebras over a field Wlodarska, A. |
| title | 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_short | Biserial minor degenerations of matrix algebras over a field |
| title_sort | biserial minor degenerations of matrix algebras over a field |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/154533 |
| work_keys_str_mv | AT wlodarskaa biserialminordegenerationsofmatrixalgebrasoverafield |