Operations on ring structures preserved by normalized automorphisms of group rings

JOURNAL OF ALGEBRA

卷:215

Article

Bleher, FM ; Chinburg, T

关键词: normalized automorphisms;    ring structures;    cohomology;   

DOI  :  10.1006/jabr.1998.7749

来源: Elsevier

【 摘 要 】

Let O be a commutative ring, and suppose sigma is a normalized O-algebra automorphism of the group ring OG of a finite group G over O. In this paper we consider the action of sigma on various algebraic structures associated to G. Suppose O is an integral domain of characteristic 0, and that no prime divisor of the order of G is invertible in O. We show that sigma preserves the lambda-ring structure of G(0)(kG) when k is a field with a ring homomorphism ? --> k. If O is the ring of integers of a number field, we show that sigma preserves the G(0)(O)(OG)-module structure of the class group Cl(OG) of OG, where G(0)(O)(BG) is the Grothendieck group of OG-lattices. (C) 1999 Academic Press.

【 授权许可】

Free