NOETHERIAN UNIQUE FACTORIZATION SEMIGROUP ALGEBRAS
Eric Jespers, Qiang Wang · Communications in Algebra · 2001
We investigate when semigroup algebras K[S] of submonoids S 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.