LAUSR

Abstract Let K be an arbitrary field and R be an arbitrary associative ring with identity 1. Slowik in [12] proved that each matrix of ± UT ( ∞ , K ) (the group of upper triangular infinite matrices whose entries lying on the main diagonal are equal to either 1 or −1) 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 ( ∞ , R ) can be expressed as a product of at most four involutions. We also prove that for the complex field every element of Ω T ( ∞ , C ) (the group of upper triangular infinite matrices whose entries lying on the main diagonal satisfy a a ‾ = 1 ) can be expressed as a product of at most three coninvolutions (matrices satisfying A A ‾ = I ).