Geodesic
Morita equivalent unital locally matrix algebras
Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 173-179.

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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
Mots-clés : Morita equivalence. 
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O. Bezushchak; B. Oliynyk. Morita equivalent unital locally matrix algebras. Algebra and discrete mathematics, Tome 29 (2020) no. 2, pp. 173-179. http://geodesic.mathdoc.fr/item/ADM_2020_29_2_a3/

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