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 α and an...
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| Date: | 2020 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2020
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/188513 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Morita equivalent unital locally matrix algebras / O. Bezushchak, B. Oliynyk // Algebra and Discrete Mathematics. — 2020. — Vol. 29, № 2. — С. 173–179. — Бібліогр.: 18 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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 α and an arbitrary not locally finite Steinitz number s there exist unital locally matrix algebras A, B such that dimF A = dimF B = α, st(A) = st(B) = s, however, the algebras A, B are not Morita equivalent. |
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