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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. Divided domains were introduced by Akiba (1967) who called them AV-domains.

References

1. Dobbs, David E. (1981), "On locally divided integral domains and CPI-overrings", International Journal of Mathematics and Mathematical Sciences, 4: 119–135, doi:10.1155/S0161171281000082

External links

• Cahen, Paul-Jean; Chabert, Jean-Luc; Dobbs, David E.; Tartarone, Francesca (2000), "On locally divided domains of the form Int(D)" (PDF), Archiv der Mathematik, 74 (3): 183–191, doi:10.1007/s000130050429, S2CID 121221904, archived from the original (PDF) on 2012-01-14
• Akiba, Tomoharu (1967), "A note on AV-domains", Bull. Kyoto Univ. Education Ser. B, 31: 1–3, MR 0218339

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