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

Year 2021, Volume: 50 Issue: 4, 1169 - 1169, 06.08.2021

Yilmaz Durğun

https://doi.org/10.15672/hujms.880852

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.

Keywords

D-extending modules, d-closed submodules, semiartinian modules

References

• [1] Y. Durğun, D-extending modules, Hacet. J. Math. Stat. 49 (3), 914-920, 2020.
• [2] A. Tercan, Modules Whose Exact Submodules Are Direct Summands, An. Şt. Univ. Ovidious Constanta 8 (2), 143-150, 2000.