Skew-symmetric Elements in Nonlinear Involutions in Group Rings  

作　　者：A.P. Raposo 

机构地区：[1]Escuela Universitaria de Arquitectura Tecnica Universidad Politecnica de Madrid, Madrid, Spain

出　　处：《Algebra Colloquium》2015年第2期321-332,共12页代数集刊（英文版）

摘　　要：Given an involution in a group G, it can be extended in various ways to an involution in the group ring RG, where R is a ring, not necessarily commutative. In this paper nonlinear extensions are considered and necessary and sufficient conditions are given on the group G, its involution, the ring R and the extension for the set of skew-symmetric elements to be commutative and for it to be anticommutative.Given an involution in a group G, it can be extended in various ways to an involution in the group ring RG, where R is a ring, not necessarily commutative. In this paper nonlinear extensions are considered and necessary and sufficient conditions are given on the group G, its involution, the ring R and the extension for the set of skew-symmetric elements to be commutative and for it to be anticommutative.

关 键 词：group ring INVOLUTION skew-symmetric element 

分 类 号：O641[理学—物理化学] TP277[理学—化学]