On locally divided integral domains and CPI-overrings

[摘要] It is proved that an integral domainRis locally divided if and only if each CPI-extension ofℬ(in the sense of Boisen and Sheldon) isR-flat (equivalently, if and only if each CPI-extension ofRis a localization ofR). 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 dimension2, and qusilocal domains with the QQR-property. The property of being CPI-closed behaves nicely with respect to theD+Mconstruction, but is not a local property.

[学科分类] 数学（综合）