Factorization of Ideals in Leavitt Path algebras

Abstract

After pointing out how ideals in a Leavitt path algebra L of a graph E behave like ideals in a commutative ring, we shall consider the question of factorizing an arbitrary ideal I as a product of finitely many special type of ideals such as the prime, irreducible and primary ideals.In this context, factorization of graded ideals seem to influence the factorization of non-graded ideals. Examples illustrate our conclusions.