Associate elements in commutative rings
This paper deals with several kinds of associateness of elements in commutative rings, and the connections between them. For example, in this paper, two elements \(a\) and \(b\) in a commutative ring \(R\) are called \textit{associates} if \(aR=bR\). The ring \(R\) is \textit{strongly associate} if for two associate elements \(a\) and \(b\), we have \(a=ub \) for a unit \(u\in R\). The authors define and study \textit{strongly regular associate rings}, they deal also with presimpliable rings (defined by A. Bouvier), etc. They relate associateness properties to other ring properties as, e.g., the bounded factorization property. The authors investigate stability of the various properties with respect to direct products, ultraproducts, etc. They also include many relevant examples.
scientific article; zbMATH DE number 6349606