On Endomorphism Rings of Leavitt Path Algebras

Abstract

Let E be an arbitrary graph, K be any eld and A be the endomorphism
ring of L := L_K(E) considered as a right L-module. Among the other
results, we prove that: (1) If A is a von Neumann regular ring, then A is dependent if and only if for any two paths in L satisfying some conditions are initial of each other, (2) If A is dependent then L_K(E) is morphic, (3) L is morphic and von Neumann regular if and only if L is semisimple and every homogeneous component is artinian.