## Abstract

This section is devoted to a very concrete problem. As usual, let K be a commutative ring with 1, and let UT their canonical representations in the free K-module of rank n. These classical objects deserve to be studied from various positions; in particular, from the standpoint of identities and varieties. Naturally, the first problem one should solve here is the following: to describe the varieties var ut

_{n}(K) = UT_{n}and T_{n}(K) = T_{n}be the full unitriangular and triangular matrix groups of degree n over K, respectively. Denote by$$
{\rm{u}}{{\rm{t}}_{\rm{n}}}{\rm{ = u}}{{\rm{t}}_{\rm{n}}}\left( {\rm{K}} \right){\rm{ = }}\left( {{{\rm{K}}^{\rm{n}}}{\rm{,U}}{{\rm{T}}_{\rm{n}}}\left( {\rm{K}} \right)} \right){\rm{ and }}{{\rm{t}}_{\rm{n}}}{\rm{ = }}{{\rm{t}}_{\rm{n}}}\left( {\rm{K}} \right){\rm{ = }}\left( {{{\rm{K}}^{\rm{n}}}{\rm{,}}{{\rm{T}}_{\rm{n}}}\left( {\rm{K}} \right)} \right)
$$

_{n}and var t_{n}or, equivalently, to find bases for the identities of the representations ut_{n}and t_{n}.## Keywords

Radical Class Nilpotent Group Wreath Product Faithful Representation Dedekind Domain
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Birkhäuser Boston 1981