Primary decompositions of unital locally matrix algebras
| Autor: | Bogdana Oliynyk, Oksana Bezushchak |
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| Rok vydání: | 2020 |
| Předmět: |
Pure mathematics
primary decomposition lcsh:Mathematics General Mathematics Unital Clifford algebra Dimension (graph theory) locally matrix algebra tensor product Computer Science::Computational Geometry lcsh:QA1-939 Primary decomposition Matrix (mathematics) Tensor product Matrix algebra clifford algebra Uncountable set steinitz number Mathematics |
| Zdroj: | Bulletin of Mathematical Sciences, Vol 10, Iss 1, Pp 2050006-1-2050006-7 (2020) |
| ISSN: | 1664-3615 1664-3607 |
| DOI: | 10.1142/s166436072050006x |
| Popis: | We construct a unital locally matrix algebra of uncountable dimension that (1) does not admit a primary decomposition, (2) has an infinite locally finite Steinitz number. It gives negative answers to questions from [V. M. Kurochkin, On the theory of locally simple and locally normal algebras, Mat. Sb., Nov. Ser. 22(64)(3) (1948) 443–454; O. Bezushchak and B. Oliynyk, Unital locally matrix algebras and Steinitz numbers, J. Algebra Appl. (2020), online ready]. We also show that for an arbitrary infinite Steinitz number [Formula: see text] there exists a unital locally matrix algebra [Formula: see text] having the Steinitz number [Formula: see text] and not isomorphic to a tensor product of finite-dimensional matrix algebras. |
| Databáze: | OpenAIRE |
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