Biserial minor degenerations of matrix algebras over a field
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Biserial minor degenerations of matrix algebras over a field
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| Creator |
Wlodarska, A.
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| 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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| Date |
2019-06-15T16:27:34Z
2019-06-15T16:27:34Z 2010 |
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| Type |
Article
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| Identifier |
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 |
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en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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