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In sharp contrast to the Abrams-Rangaswamy Theorem that the only von Neumannregular Leavitt path algebras are exactly those associated to acyclic graphs,here we prove that the Leavitt path algebra of any arbitrary graph is a gradedvon Neumann regular ring. Several properties of Leavitt path algebras, such astriviality of the Jacobson radical, flatness of graded modules and finitelygenerated graded right (left) ideals being generated by an idempotent element,follow as a consequence of general theory of grade von Neumann regular rings.

Leavitt path algebras are graded von Neumann regular rings