Consider a field k of characteristic zero. Let Q = (qij) be a n× n-matrix with the entries qij ∈ k∗ or qij is an indeterminate, satisfying qijqji = qii = 1. The algebra k[Q] is generated by k and q ij , i, j = 1, . . . , n. Denote k(Q) = Fract(k[Q]) and Γ is the subgroup in k(Q) generated by k and the entries of Q. Throughout the paper R is a k-algebra with a unit. Definition 1.1. We say that R...