Centrally Essential Torsion-Free Rings of Finite Rank

TL;DR

This paper investigates the properties of centrally essential torsion-free rings of finite rank, revealing their quasi-invariance and faithfulness of associated Abelian groups, with implications for algebraic structure classification.

Contribution

It establishes that such rings are quasi-invariant but not necessarily invariant, and shows torsion-free Abelian groups with these rings are faithful.

Findings

Centrally essential rings of finite rank are quasi-invariant.

Such rings are not necessarily invariant.

Torsion-free Abelian groups with these rings are faithful.

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 paper will appear in Beitr\"age zur Algebra und Geometrie / Contributions to Algebra and Geometry.