@article{article_1478925, title={The ring $R\{X\}$}, journal={International Electronic Journal of Algebra}, volume={37}, pages={36–43}, year={2025}, DOI={10.24330/ieja.1478925}, author={Abuosba, Emad and Al-azaizeh, Mariam}, keywords={Prime ideal, localization, over ring, polynomial ring, Prüfer conditions}, abstract={Let $R$ be a commutative ring with unity and $W=\{f(X)\in R[X]:f(0)=1\}$. We define $R\{X\}=W^{-1}R[X]$. We show that the maximal ideals of $R\{X\} $ are of the form $W^{-1}(M,X)$ where $M$ is a maximal ideal of $R$, and so if $R$ is finite dimensional, then $\dim R\{X\}=\dim R[X]$. We show that $R\{X\}$ is a Prüfer ring if and only if $R$ is a von Neumann regular ring, and so if $R\{X\}$ satisfies one of the Prüfer conditions, it satisfies all of them.}, number={37}, publisher={Abdullah HARMANCI}