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arXiv · 2204.02528

Prime Principal Right Ideal Rings

Tamem Al-Shorman·Malik Bataineh
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Abstract

Let R be a commutative ring with unity $1\in R$. In this article, we introduce the concept of prime principal right ideal rings (\textbf{PPRIR}), A prime ideal P of R is said to be prime principal right ideal (\textbf{PPRI}) is given by $P =\{ ar : r\in R\}$ for some element a. The ring R is said to be prime principal right ideal ring (\textbf{PPRIR}) if every prime ideal of R is a prime principal right ideal (\textbf{PPRI}). A prime principal right ideal ring R is called a prime principal right ideal domain (\textbf{PPRID}) if R is a domain. Several properties and characteristics of prime principal right ideal ring (\textbf{PPRIR}).

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Tamem Al-Shorman, Malik Bataineh. 2022-04-06. Prime Principal Right Ideal Rings. https://arxiv.org/abs/2204.02528

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