Torsion-free rings with almost regular automorphisms

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In this paper we consider finite rank torsion-free rings, which have almost regular automorphisms (a non-trivial automorphism is calledalmost regular if it has only trivial fixed points, i.e. zero and the elements of a ring linear dependent on its identity). The main results of this paper are the characterization of some types of rings which have almost regular automorphism of the finite order (the analogue of known G.Higman’s Theorem[l]) and the characterization of all rings, all of whose non-trivial automorphisms are almost regular.