Abstract:
One class of varieties of algebras is defined, where the group of tame automorphisms of free two-generated algebras admits the structure of an amalgamated free product over an arbitrary integrity domain. Proved the reducibility of tame automorphisms of free two-generated algebras of these varieties over Euclidean domains. It is proved that the generalization of Nagata automorphism is a wild automorphism of free algebras of these varieties from two variables over Euclidean domains.
Keywords:automorphism, tame automorphism, free product of groups, euclidean domain.
