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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| Date: | 2010 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2010
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.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| Summary: | 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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