Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5773141 | Linear Algebra and its Applications | 2017 | 9 Pages |
Abstract
Let K be an arbitrary field and R be an arbitrary associative ring with identity 1. SÅowik in [12] proved that each matrix of ±UT(â,K) (the group of upper triangular infinite matrices whose entries lying on the main diagonal are equal to either 1 or â1) can be expressed as a product of at most five involutions. In this article, we extend the investigate to an arbitrary associative ring R with identity 1. Our conclusion is that every element of ±UT(â,R) can be expressed as a product of at most four involutions. We also prove that for the complex field every element of ΩT(â,C) (the group of upper triangular infinite matrices whose entries lying on the main diagonal satisfy aaâ¾=1) can be expressed as a product of at most three coninvolutions (matrices satisfying AAâ¾=I).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Xin Hou, Shangzhi Li, Qingqing Zheng,