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On locally divided integral domains and CPI-overrings

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  • David E. Dobbs

Abstract

It is proved that an integral domain R is locally divided if and only if each CPI-extension of ℬ (in the sense of Boisen and Sheldon) is R -flat (equivalently, if and only if each CPI-extension of R is a localization of R ). Thus, each CPI-extension of a locally divided domain is also locally divided. Treed domains are characterized by the going-down behavior of their CPI-extensions. A new class of (not necessarily treed) domains, called CPI-closed domains, is introduced. Examples include locally divided domains, quasilocal domains of Krull dimension 2 , and qusilocal domains with the QQR-property. The property of being CPI-closed behaves nicely with respect to the D + M construction, but is not a local property.

Suggested Citation

  • David E. Dobbs, 1981. "On locally divided integral domains and CPI-overrings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 4, pages 1-17, January.
    • Handle: RePEc:hin:jijmms:108278
    DOI: 10.1155/S0161171281000082
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