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In this paper we describe three different variations of prime ideals:strongly irreducible ideals, strongly prime ideals and insulated prime idealsin the context of Leavitt path algebras. We give necessary and sufficientconditions under which a proper ideal of a Leavitt path algebra $L$ is aproduct as well as an intersection of finitely many of these different types ofprime ideals. Such factorizations, when they are irredundant, are shown to beunique except for the order of the factors. We also characterize the Leavittpath algebras $L$ in which every ideal admits such factorizations and also inwhich every ideal is one of these special type of ideals.

Variations of primeness and Factorization of ideals in Leavitt Path Algebras