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This article is cited in 1 scientific paper (total in 1 paper)
RESEARCH ARTICLE
Morita equivalent unital locally matrix algebras
O. Bezushchaka, B. Oliynykb a Faculty of Mechanics and Mathematics,Taras Shevchenko National University of Kyiv, Volodymyrska, 60, Kyiv 01033, Ukraine
b Department of Mathematics, National University of Kyiv-Mohyla Academy, Skovorody St. 2, Kyiv, 04070, Ukraine
Abstract:
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.
Keywords:
locally matrix algebra, Steinitz number, Morita equivalence.
Received: 09.02.2020
Citation:
O. Bezushchak, B. Oliynyk, “Morita equivalent unital locally matrix algebras”, Algebra Discrete Math., 29:2 (2020), 173–179
Linking options:
https://www.mathnet.ru/eng/adm750 https://www.mathnet.ru/eng/adm/v29/i2/p173
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