Locally unit conditions of endomorphism rings of leavitt path algebras

Let E be a directed graph, K any field, L ≔L_K (E) coefficients are Leavitt path algebras taken from field, K of the graph E and H≔End(L_L) be the endomorphism ring with units formed over the right modules of the Leavitt path algebras. In this study, the definition of the left locally unit regular ring is given. In addition, if H is a locally unit regular ring, L is a left and right regular local unit ring, if L is morphic and image-projective, H is also a left morphic, if H is a directly finite ring, L is a directly finite ring. Finally, it has been proved that if the H exchange ring is L is a directly finite ring and L is a directly finite ring, L must be an exchange ring.