Products of ideals in Leavitt path algebras

Abstract

Ideals in Leavitt path algebras share many properties with those of integral domains. Since studying factorizations of ideals in integral domains into special types of ideals (e.g., prime, prime-power, primary, irreducible, semiprime, quasi-primary) has proved fruitful, we conduct an analogous investigation for Leavitt path algebras. Specifically, we classify the proper ideals in these rings that admit factorizations into products of each of the above types. We also classify the Leavitt path algebras where every proper ideal admits a factorization of these sorts, as well as those Leavitt path algebras where every proper ideal is of one of those types.