Defining relations in generalized elementary m-unit triangular groups over an associative ring

In this paper, we find the forming elements and defining relations of a generalized elementary m-triangular group UT Em o ( ℵ, R ) of degree ℵ≥2 over an arbitrary associative ring . In solving this problem, the method of letter transformation is used, developed by one of the authors in his earlier works. The group studied in this paper turned out to be closely related to another issue of algebra with radical rings. Using some of the intermediate results of the work, some new examples (both simple and complex) of matrix radical rings are also found here.