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.^[1] Divided domains were introduced by Akiba (1967) who called them AV-domains.

References

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

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 No., 31: 1–3, MR 0218339

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Divided domain

See also

References