If-automorphisms of a free solvable S_ p-permutable algebra of a finite rank over a left cancellative monoid are pseudo-tame

摘要

Consider a variety V of acts over a left cancellative monoid S that have a ternary Maltsev operation p (〈p, S〉-algebras). Using the Magnus Artamonov representation, the construction of the free Abelian extension of an arbitrary V-algebra was obtained and explored by the author. In the present article we prove that each IF-automorphism of a free k-step solvable V-algebra of a finite rank (k > 1) is pseudo-tame, i.e. it is presented as a product of elementary automorphisms of a special module over a ring with several objects.