Divided domain

In algebra, a divided domain is an integral domain R in which every prime ideal $\mathfrak{𝔭}$ satisfies $\mathfrak{𝔭}=\mathfrak{𝔭}{R}_{\mathfrak{𝔭}}$. 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. Divided domains were introduced by (Akiba 1967) who called them AV-domains.

External links

• Cahen, Paul-Jean; Chabert, Jean-Luc; Dobbs, David E.; Tartarone, Francesca (2000), "On locally divided domains of the form Int(D)", Archiv der Mathematik 74 (3): 183–191, doi:10.1007/s000130050429, http://www.latp.cahen.u-3mrs.fr/Recherche/Pubs/locdiv.pdf 
• Akiba, Tomoharu (1967), "A note on AV-domains", Bull. Kyoto Univ. Education Ser. B 31: 1–3