NOETHERIAN UNIQUE FACTORIZATION SEMIGROUP ALGEBRAS

Abstract

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.

ACKNOWLEDGMENT

This work is supported in part by research grant OGP0036631, NSERC Canada, Onderzoeksraad Vrije Universiteit Brussel and Fonds voor Wetenschappelijk Onderzoek.