Skew-symmetric Elements in Nonlinear Involutions in Group Rings

• 作者: A.P. Raposo
• 来源期刊: 代数集刊:英文版
• 学科: 化学
• 关键词: 非线性扩展 对称元素 对合 充分条件 可交换 群环
• 年，卷（期）: 2015,（2）
• 页码范围: 321-332
• 页数: 12页
• 分类号: O641
• 语种: 中文

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.