In algebra, a divided domain is an integral domain R in which every prime ideal satisfies . 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
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