Centrally Essential Torsion-Free Rings of Finite Rank

Abstract

It is proved that centrally essential rings, whose additive groups of finite rank are torsion-free groups of finite rank, are quasi-invariant but not necessarily invariant. Torsion-free Abelian groups of finite rank with centrally essential endomorphism rings are faithful.The work of O.V. Lyubimtsev is done under the state assignment No 0729-2020-0055. A.A. Tuganbaev is supported by Russian Scientific Foundation, project 16-11-10013P.