Modular Species and Prime Ideals for the Ring of Monomial Representations of a Finite Group#

The ring of monomial representations of a finite group has been investigated by Dress (1971 Dress , A. W. M. ( 1971 ). The ring of monomial representations I: structure theory . J. Algebra 18 : 137 – 157 . CSA] CROSSREF]  Google Scholar]) and Boltje (1990 Boltje , R. ( 1990 ). A canonical Brauer induction formula . Astérisque 181–182 : 31 – 59 . Google Scholar]), among others. It is of interest in connection with induction theorems in representation theory. Its species have recently been determined by Boltje. In this article, we will analyze the block distribution of species. As an application, we will determine the prime ideals of the ring of monomial representations. The results here constitute a slightly modified version of part of the first author's Diplomarbeit (Fotsing, 2003 Fotsing , B. ( 2003 ). Zum Ring der monomialen Darstellungen einer endlichen Gruppe . Diplomarbeit . Jena . Google Scholar]), written under the direction of the second author.