On the ring of inertial endomorphisms of an abelian group
  An endomorphisms $\varphi$ of an abelian group $A$ is said inertial if each subgroup $H$ of $A$ has finite index in $H+\varphi (H)$.   We study the ring of inertial endomorphisms of an abelian group. Here we obtain a satisfactory description modulo the ideal of finitary endomorphisms.   Also the corresponding problem for vector spaces is considered.   For the characterization of inertial endomorphisms of an abelian group see arXiv:1310.4625 .   The group of invertible inertial endomorphisms has been studied in arXiv:1403.4193 . 
Ulderico Dardano, Silvana Rinauro
math.GR