Divided domain

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

## References

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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

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* 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 2012-01-14Int(D)&rft.volume=74&rft.issue=3&rft.pages=183-191&rft.date=2000&rft_id=info:doi/10.1007/s000130050429&rft_id=https://api.semanticscholar.org/CorpusID:121221904#id-name=S2CID&rft.aulast=Cahen&rft.aufirst=Paul-Jean&rft.au=Chabert,+Jean-Luc&rft.au=Dobbs,+David+E.&rft.au=Tartarone,+Francesca&rft_id=http://www.latp.cahen.u-3mrs.fr/Recherche/Pubs/locdiv.pdf&rfr_id=info:sid/en.wikipedia.org:Divided+domain" class="Z3988">
* Akiba, Tomoharu (1967), "A note on AV-domains", Bull. Kyoto Univ. Education Ser. B, 31: 1–3, MR 0218339

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