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Von Neumann regularity of some locally finite-dimensional algebras is studied. C. Lanski has asked  whether every simple algebraic algebra over a field is von Neumann regular. Along the same lines, Handelman asks whether a regular locally finite-dimensional algebra is locally semisimple. In this note we answer Lanski's question in the negative and discuss some of the subtleties of the second problem.doi:10.2307/2043466 fatcat:lf6ouigdfbg2zmwzupaxhmpmn4