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Morita equivalent unital locally matrix algebras

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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Bibliographic Details
Main Authors: Bezushchak, O., Oliynyk, B.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2020
Subjects:
locally matrix algebra
Steinitz number
Morita equivalence
03C05
03C60
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1545
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spelling 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
first_indexed 2024-04-12T06:25:12Z
last_indexed 2024-04-12T06:25:12Z
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