On locally divided integral domains and CPI-overrings
1981 ◽
Vol 4
(1)
◽
pp. 119-135
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Keyword(s):
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.
2005 ◽
Vol 04
(06)
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pp. 599-611
Keyword(s):
2019 ◽
Vol 18
(01)
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pp. 1950018
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Keyword(s):
2015 ◽
Vol 58
(3)
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pp. 449-458
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1999 ◽
Vol 129
(1)
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pp. 77-84
Keyword(s):
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2016 ◽
Vol 95
(1)
◽
pp. 14-21
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2011 ◽
Vol 18
(spec01)
◽
pp. 965-972
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1978 ◽
Vol 21
(3)
◽
pp. 373-375
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Keyword(s):