Divided domain

In algebra, a divided domain is an integral domain R in which every prime ideal [math]\displaystyle{ \mathfrak{p} }[/math] satisfies [math]\displaystyle{ \mathfrak{p} = \mathfrak{p} R_\mathfrak{p} }[/math]. 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

• https://web.archive.org/web/20120114162738/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