Primary decompositions of unital locally matrix algebras
| dc.contributor.author | Bezushchak, Oksana | |
| dc.contributor.author | Oliynyk, Bogdana | |
| dc.date.accessioned | 2021-02-04T21:28:37Z | |
| dc.date.available | 2021-02-04T21:28:37Z | |
| dc.date.issued | 2020 | |
| dc.description.abstract | 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 s there exists a unital locally matrix algebra A having the Steinitz number s and not isomorphic to a tensor product of finite-dimensional matrix algebras. | en_US |
| dc.identifier.citation | Bezushchak O. Primary decompositions of unital locally matrix algebras [electronic resource] / Bezushchak O., Oliynyk B. // Bulletin of Mathematical Sciences. - 2020. - Vol. 10, Issue 1. - Article number 2050006. | en_US |
| dc.identifier.uri | https://doi.org/10.1142/S166436072050006X | |
| dc.identifier.uri | https://ekmair.ukma.edu.ua/handle/123456789/19412 | |
| dc.language.iso | en | uk_UA |
| dc.relation.source | Bulletin of Mathematical Sciences. | en_US |
| dc.status | first published | uk_UA |
| dc.subject | Locally matrix algebra | en_US |
| dc.subject | primary decomposition | en_US |
| dc.subject | Steinitz number | en_US |
| dc.subject | tensor product | en_US |
| dc.subject | Clifford algebra | en_US |
| dc.subject | article | en_US |
| dc.title | Primary decompositions of unital locally matrix algebras | en_US |
| dc.type | Article | uk_UA |
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