Quasi-Baer * -Ring Characterization of Leavitt Path Algebras

We say that a graded ring (& lowast;-ring) Ris a graded quasi-Baer ring (graded quasi-Baer & lowast;-ring)if, for each graded idealIofR, the right annihilator ofIis generated by a homogeneous idempotent(projection). We prove that a Leavitt path algebra is quasi-Baer (quasi-Baer & lowast;) if and only if it is gradedquasi-Baer (graded quasi-Baer & lowast;). We show that a Leavitt path algebra is quasi-Baer (quasi-Baer & lowast;)if its zero component is quasi-Baer (quasi-Baer & lowast;). However, we give some example that showing thatthe converse implication fails. Finally, we characterize the Leavitt path algebras that are quasi-Baer & lowast;-rings in terms of the properties of the underlying graph.