Primitivity of prime countable-dimensional regular algebras

Abstract

Let $k$ be a field and let $R$ be a countable dimensional prime von Neumann regular $k$-algebra. We show that $R$ is primitive, answering a special case of a question of Kaplansky.

8 pages; revised version; to appear in Proc. Amer. Math. Soc

References in corpus (1)

• Dynamical systems associated to separated graphs, graph algebras, and paradoxical decompositions