Prime principal right ideal rings
type: Item
instance of: scholarly article
title: Prime principal right ideal rings
zbMATH Open document ID: 1546.1303
DOI: 10.35834/2024/3601010
author: Tamem al-Shorman
author: Malik Bataineh
published in: Missouri Journal of Mathematical Sciences
publication date: 2024-08-12T00:00:00Z
review text: Let \(R\) be a commutative ring with a nonzero identity element 1. An ideal \(P\) in \(R\) is called a prime ideal if for all \( x,y\in R\), whenever \(xy \in P\), it follows that either \(x \in P\) or \(y \in P\). The ideal \(P\) is said to be a principal right ideal if \(P = \{ar : r \in R\}\) for some element \(a \in R\). A ring \(R\) is called a principal right ideal ring if every right ideal of \(R\) is a principal right ideal, and \(R\) is referred to as a principal right ideal domain if it is also an integral domain. In this article, the authors explore various properties and characteristics of prime principal right ideal rings.
reviewed by: Jebrel M. Habeb
Mathematics Subject Classification ID: 13F10
Mathematics Subject Classification ID: 13G99
zbMATH DE Number: 7895241
zbMATH Keywords: prime principal right ideal ring
zbMATH Keywords: prime principal right ideal domain
MaRDI profile type: Publication
cites work: Q3154382
cites work: Pseudo-valuation domains
cites work: Q3236717
cites work: Principal Right Ideal Rings
cites work: Q4117922
description: scientific article; zbMATH DE number 7895241