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Operations on Ring Structures Preserved by Normalized Automorphisms of Group Rings
Journal article   Open access   Peer reviewed

Operations on Ring Structures Preserved by Normalized Automorphisms of Group Rings

Frauke M Bleher and Ted Chinburg
Journal of algebra, Vol.215(2), pp.531-542
05/15/1999
DOI: 10.1006/jabr.1998.7749
url
https://doi.org/10.1006/jabr.1998.7749View
Published (Version of record) Open Access

Abstract

Let O be a commutative ring, and suppose σ is a normalized O-algebra automorphism of the group ring OGof a finite groupGover O. In this paper we consider the action of σ on various algebraic structures associated toG. Suppose O is an integral domain of characteristic 0, and that no prime divisor of the order ofGis invertible in O. We show that σ preserves the λ-ring structure of G0(kG) whenkis a field with a ring homomorphism O→k. If O is the ring of integers of a number field, we show that σ preserves the GO0(OG)-module structure of the class group Cl(OG) of OG, where GO0(OG) is the Grothendieck group of OG-lattices.
cohomology ring structures normalized automorphisms

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