@article{Baeck2022, 
author = {Jongwook Baeck},
title = {On    S-principal right ideal rings},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {7},
pages = {12106-12122},
keywords = {S-principal right ideal ring, S-principal right ideal domain, right S-Noetherian ring, S-principal right ideal, Eakin-Nagata-Eisenbud theorem, Cohen's theorem},
url = {https://www.sciopen.com/article/10.3934/math.2022673},
doi = {10.3934/math.2022673},
abstract = {Let    S be a multiplicative subset of a ring    R. A right ideal    A of    R is referred to as    S-principal if there exist an element    s  ∈  S and a principal right ideal    a  R of    R such that    A  s  ⊆  a  R  ⊆  A. A ring is referred to as an    S-principal right ideal ring (   S-PRIR) if every right ideal is    S-principal. This paper examines    S-PRIRs, which extend the notion of principal right ideal rings. Various examples, including several extensions of    S-PRIRs are investigated, and some practical results are proven. A noncommutative    S-PRIR that is not a principal right ideal ring is found, and the    S-variants of the Eakin-Nagata-Eisenbud theorem and Cohen's theorem for    S-PRIRs are proven.}
}