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

Zachary Mesyan, Kulumani M. Rangaswamy
2021 arXiv   pre-print
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
more » ... into products or intersections of finitely many completely irreducible ideals.
arXiv:2101.05376v1 fatcat:qpblm2u4wrhnpct6h6ihwfkwue