Addendum to "D-extending modules" [Hacet. J. Math. Stat. 49(3), 914-920, 2020]

Abstract

After the paper [1] was published, the following information about D-extending modules was pointed out by Adnan Tercan. Let $r$ be a left exact preradical in the category of right $R$-modules and let $M$ be a right $R$-module. A submodule $N$ of $M$ is called exact in $M$ provided $r(M/N)=0$. A module $M$ is called an ES-module provided every exact submodule of $M$ is a direct summand of $M$. ES-modules was introduced by A. Tercan in [2]. Since socle is left exact preradical, ES-modules coincide with D-extending modules for $r=Soc$.The author who first noticed the ES-module via personal communication with A. Tercan would like to thank him for this reference.