Morita equivalent unital locally matrix algebras

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 dimF A = dimF B = α, st(A) = st(B) = s, however, the algebras A, B are not Morita equivalent.