Submonoids of Polycyclic-by-Finite Groups and their Algebras
by Jespers, Eric; Okniński, Jan
We describe Noetherian semigroup algebras K[S] of submonoids S of polycyclic-by-finite groups over a field K. As an application, we show that these algebras are finitely presented and also that they are Jacobson rings. Next we show that every prime ideal P of K[S] is strongly related to a prime ideal of the group algebra of a subgroup of the quotient group of S via a generalised matrix ring structure on K[S]/P. Applications to the classical Krull dimension, prime spectrum, and irreducible K[S]-modules are given.
DOI: 10.1023/A:1011433816487
Print publication date: 6/1/2001
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