Products and Intersections of Prime-Power Ideals in Leavitt Path Algebras

Abstract

We continue a very fruitful line of inquiry into the multiplicative ideal theory of an arbitrary Leavitt path algebra L. Specifically, we show that factorizations of an ideal in L into irredundant products or intersections of finitely many prime-power ideals are unique, provided that the ideals involved are powers of distinct prime ideals. We also characterize the completely irreducible ideals in L, which turn out to be primepower ideals of a special type, as well as ideals that can be factored into products or intersections of finitely many completely irreducible ideals.