Prime principal right ideal rings
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.
scientific article; zbMATH DE number 7895241