  Let E be an arbitrary directed graph and let K be any field. It is shown that
the Leavitt path algebra A of the graph E over the field K is a Zorn ring if
and only if the graph E satisfies the Condition (L), that is, every cycle in E
has an exit. It is also shown that the Leavitt path algebra A is a weakly
regular ring if and only if every homomorphic image of A is a Zorn ring. The
corresponding statement for graph C*-algebras is also investigated.
