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.
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Notes
It is clear that a ring R with center C is centrally essential if and only if the module \(R_{C}\) is an essential extension of the module \(C_{C}\).
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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.
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Lyubimtsev, O.V., Tuganbaev, A.A. Centrally essential torsion-free rings of finite rank. Beitr Algebra Geom 62, 615–622 (2021). https://doi.org/10.1007/s13366-020-00529-0
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DOI: https://doi.org/10.1007/s13366-020-00529-0