Morita equivalent unital locally matrix algebras
We describe Morita equivalence of unital locally matrix algebras in terms of their Steinitz parametrization. Two countable-dimensional unital locally matrix algebras are Morita equivalent if and only if their Steinitz numbers are rationally connected. For an arbitrary uncountable dimension \(\alpha\...
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| Дата: | 2020 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2020
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1545 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-15452020-07-08T07:13:20Z Morita equivalent unital locally matrix algebras Bezushchak, O. Oliynyk, B. locally matrix algebra, Steinitz number, Morita equivalence 03C05, 03C60 We describe Morita equivalence of unital locally matrix algebras in terms of their Steinitz parametrization. Two countable-dimensional unital locally matrix algebras are Morita equivalent if and only if their Steinitz numbers are rationally connected. For an arbitrary uncountable dimension \(\alpha\) and an arbitrary not locally finite Steinitz number \(s\) there exist unital locally matrix algebras \(A\), \(B\) such that \(\dim_{F}A=\dim_{F}B=\alpha\), \(\mathbf{st}(A)=\mathbf{st}(B)=s\), however, the algebras \(A\), \(B\) are not Morita equivalent. Lugansk National Taras Shevchenko University The second author was partially supported by the grant for scientific researchers of the ``Povir u sebe'' Ukranian Foundation 2020-07-08 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1545 10.12958/adm1545 Algebra and Discrete Mathematics; Vol 29, No 2 (2020) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1545/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1545/666 Copyright (c) 2020 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
locally matrix algebra Steinitz number Morita equivalence 03C05 03C60 |
| spellingShingle |
locally matrix algebra Steinitz number Morita equivalence 03C05 03C60 Bezushchak, O. Oliynyk, B. Morita equivalent unital locally matrix algebras |
| topic_facet |
locally matrix algebra Steinitz number Morita equivalence 03C05 03C60 |
| format |
Article |
| author |
Bezushchak, O. Oliynyk, B. |
| author_facet |
Bezushchak, O. Oliynyk, B. |
| author_sort |
Bezushchak, O. |
| title |
Morita equivalent unital locally matrix algebras |
| title_short |
Morita equivalent unital locally matrix algebras |
| title_full |
Morita equivalent unital locally matrix algebras |
| title_fullStr |
Morita equivalent unital locally matrix algebras |
| title_full_unstemmed |
Morita equivalent unital locally matrix algebras |
| title_sort |
morita equivalent unital locally matrix algebras |
| description |
We describe Morita equivalence of unital locally matrix algebras in terms of their Steinitz parametrization. Two countable-dimensional unital locally matrix algebras are Morita equivalent if and only if their Steinitz numbers are rationally connected. For an arbitrary uncountable dimension \(\alpha\) and an arbitrary not locally finite Steinitz number \(s\) there exist unital locally matrix algebras \(A\), \(B\) such that \(\dim_{F}A=\dim_{F}B=\alpha\), \(\mathbf{st}(A)=\mathbf{st}(B)=s\), however, the algebras \(A\), \(B\) are not Morita equivalent. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2020 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1545 |
| work_keys_str_mv |
AT bezushchako moritaequivalentunitallocallymatrixalgebras AT oliynykb moritaequivalentunitallocallymatrixalgebras |
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2024-04-12T06:25:12Z |
| last_indexed |
2024-04-12T06:25:12Z |
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1796109246601887744 |