Divided domain

In algebra, a divided domain is an integral domain R in which every prime ideal ${\displaystyle {\mathfrak {p}}}$ satisfies ${\displaystyle {\mathfrak {p}}={\mathfrak {p}}R_{\mathfrak {p}}}$. A locally divided domain is an integral domain that is a divided domain at every maximal ideal. A Prüfer domain is a basic example of a locally divided domain.^[1] Divided domains were introduced by Akiba (1967) who called them AV-domains.