On locally divided integral domains and CPI-overrings

Autor:	David E. Dobbs
Jazyk:	angličtina
Rok vydání:	1981
Předmět:	integral domain prime ideal CPI-extension flat over-ring localization locally divided going-down treed quasilocal QQR-property Δ-domain D+M construction Krull direction. Mathematics QA1-939
Zdroj:	International Journal of Mathematics and Mathematical Sciences, Vol 4, Iss 1, Pp 119-135 (1981)
Druh dokumentu:	article
ISSN:	0161-1712 1687-0425 01611712
DOI:	10.1155/S0161171281000082
Popis:	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.
Databáze:	Directory of Open Access Journals
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