Principally-Injective Leavitt Path Algebras over Arbitrary Graphs

Abstract

In this paper we show that for any arbitrary graph E and for a field K, principally-injective conditions for the Leavitt path algebra L K (E) are equivalent to that graph E being acyclic. We also show that the principally-injective Leavitt path algebras are precisely the von Neumann regular Leavitt path algebras.