We investigate when semigroup algebras K[S] of submonoids 5 of torsion free polycyclic-by-finite groups G are Noetherian unique factorization rings in the sense of Chatters and Jordan, that is, every prime ideal contains a principal height one prime ideal. For the group algebra K[G] this problem was solved by Brown.

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Persistent URL dx.doi.org/10.1081/AGB-100107954
Journal Communications in Algebra
Jespers, E. (Eric), & Wang, Q. (2001). Noetherian unique factorization semigroup algebras. Communications in Algebra, 29(12), 5701–5715. doi:10.1081/AGB-100107954