Centrally Essential Endomorphism Rings of Abelian Groups

2019/10/02 by Lyubimtsev, Oleg, Tuganbaev, Askar
#16R99 #20K30 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1910.01222

Abstract

We study Abelian groups A with centrally essential endomorphism ring End A. If A is a such group which is either a torsion group or a non-reduced group, then the ring End A is commutative. We give examples of Abelian torsion-free groups of finite rank with non-commutative centrally essential endomorphism rings. The paper will appear in Communications in Algebra.

Related

• Centrally Essential Torsion-Free Rings of Finite Rank
• Endomorphisms of nilpotent groups of finite rank
• Generalized E-Rings
• Completely Centrally Essential Rings
• Fuchs' problem for endomorphisms of abelian groups