Semigroup Algebras of Submonoids of Polycyclic-by-Finite Groups and Maximal Orders

Necessary and sufficient conditions are given for
a prime Noetherian algebra K[S] of a submonoid
S of a polycyclic-by-finite group G to be a
maximal order. These conditions are entirely in
terms of the monoid S. This extends earlier
results of Brown concerned with the group ring
case and of the authors for the case where K[S]
satisfies a polynomial identity.

Publication year:2009

Keywords:semigroup algebra, prime ideal, polycyclic-by-finite group, maximal order