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arXiv · 2101.05376

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

Zachary Mesyan·Kulumani M. Rangaswamy
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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 prime-power ideals of a special type, as well as ideals that can be factored into products or intersections of finitely many completely irreducible ideals.

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Zachary Mesyan, Kulumani M. Rangaswamy. 2021-01-13. Products and Intersections of Prime-Power Ideals in Leavitt Path Algebras. https://doi.org/10.1142/s0219498822501043

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