Divided domain

In algebra, a divided domain is an integral domain R in which every prime ideal ${\mathfrak {p}}$ 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.

See also

• CPI extension

References

1. http://downloads.hindawi.com/journals/ijmms/1981/108278.pdf

• 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 No., 31: 1–3, MR 0218339