REGULAR IDEALS OF GRAPH ALGEBRAS

Let C*(E) be the graph C*-algebra of a row-finite graph E. We give a complete description of the vertex sets of the gauge-invariant regular ideals of C*(E). It is shown that when E satisfies condition (L), the regular ideals C*(E) are a class of gauge-invariant ideals which preserve condition (L) under quotients. That is, we show that if E satisfies condition (L) then a regular ideal J C*(E) is necessarily gaugeinvariant. Further, if J C*(E) is a regular ideal, it is shown that C*(E)/J C*(F), where F satisfies condition (L).