Morita equivalent unital locally matrix algebras

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Date
2020
Authors
Bezushchak, Oksana
Oliynyk, Bogdana
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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 α and an arbitrary not locally finite Steinitz number s there exist unital locally matrix algebras A, B such that dimFA=dimFB=α, st(A)=st(B)=s, however, the algebras A, B are not Morita equivalent.
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Keywords
locally matrix algebra, Steinitz number, Morita equivalence, article
Citation
Bezushchak O. Morita equivalent unital locally matrix algebras [electronic resource] / Bezushchak O., Oliynyk B. // Algebra and Discrete Mathematics. - 2020. - Vol. 29, Issue 2. - P. 173-179.