This article is cited in 1 paper

RESEARCH ARTICLE

Morita equivalent unital locally matrix algebras

O. Bezushchak^a, B. Oliynyk<sup>b

a</sup> 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.

MSC: 03C05, 03C60

Received: 09.02.2020

Language: English

DOI: 10.12958/adm1545

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