On Locally Unit Regularity Conditions for Arbitrary Leavitt Path Algebras

Abstract

Abstract. Let be a graph, K be any …eld and S be the endomorphism ring of L := L K ( ) considered as a right L-module. In this paper, we give de…nation of the left locally unit regular ring. We show that (1) if S is locally unit regular, then L is locally unit regular, (2) if L is morphic and image projective then S is left morphic, (3) S is a directly …nite ring then L is directly …nite, (4) if S is an exchange ring then L is directly …nite and if L is a directly …nite ring then L is an exchange ring.