Characterizing Rickart and Baer ultragraph Leavitt path algebras

Abstract

We characterize ultragraph Leavitt path algebras that are Rickart, locally Rickart, graded Rickart, and graded Rickart *-rings. We also characterize ultragraph Leavitt path algebras that are Baer, locally Baer, graded Baer, Baer *-rings, and combinations of these. These characterizations build on and generalize the work of Hazrat and Vas on Leavitt path algebras over fields to ultragraph Leavitt path algebras over semi-simple commutative unital rings.