%0 Journal Article
%T On locally divided integral domains and CPI-overrings
%A David E. Dobbs
%J International Journal of Mathematics and Mathematical Sciences
%D 1981
%I Hindawi Publishing Corporation
%R 10.1155/s0161171281000082
%X It is proved that an integral domain R is locally divided if and only if each CPI-extension of  бщ     (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.
%K integral domain
%K prime ideal
%K CPI-extension
%K flat over-ring
%K localization
%K locally divided
%K going-down
%K treed
%K quasilocal
%K QQR-property
%K жд-domain
%K D+M construction
%K Krull direction.
%U http://dx.doi.org/10.1155/S0161171281000082