ALMOST PERFECT LOCAL DOMAINS AND THEIR DOMINATING ARCHIMEDEAN VALUATION DOMAINS
2002 ◽
Vol 01
(04)
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pp. 451-467
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Keyword(s):
A commutative ring R is said to be almost perfect if R/I is perfect for every nonzero ideal I of R. We prove that an almost perfect local domain R is dominated by a unique archimedean valuation domain V of its field of quotients Q if and only if the integral closure of R contains an ideal of V. We show how to construct almost perfect local domains dominated by finitely many archimedean valuation domains. We provide several examples illustrating various possible situations. In particular, we construct an almost perfect local domain whose maximal ideal is not almost nilpotent.
2003 ◽
Vol 46
(1)
◽
pp. 3-13
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Keyword(s):
2012 ◽
Vol 11
(02)
◽
pp. 1250027
Keyword(s):
1955 ◽
Vol 51
(2)
◽
pp. 252-253
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Keyword(s):
1981 ◽
Vol 33
(1)
◽
pp. 116-128
◽
Keyword(s):
1996 ◽
Vol 61
(3)
◽
pp. 377-380
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Keyword(s):
1982 ◽
Vol 34
(1)
◽
pp. 169-180
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Keyword(s):
1981 ◽
Vol 33
(5)
◽
pp. 1232-1244
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Keyword(s):