Pairs of domains where all intermediate domains are Noetherian
Author:
Adrian R. Wadsworth
Journal:
Trans. Amer. Math. Soc. 195 (1974), 201211
MSC:
Primary 13G05
MathSciNet review:
0349665
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Abstract: For Noetherian integral domains R and T with is called a Noetherian pair (NP) if every domain A, , is Noetherian. When (Krull dimension) it is shown that the only NP's are those given by the KrullAkizuki Theorem. For , there is another type of NP besides the finite integral extension, namely where . Further, for every NP (R, T) with there is an integral NP extension B of R with . In all known examples B can be chosen to be a finite integral extension of R. For such NP's it is shown that the NP relation is transitive. T may itself be an infinite integral extension R, though, and an example of this is given. It is unknown exactly which infinite integral extensions are NP's.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029947197403496652
PII:
S 00029947(1974)03496652
Keywords:
Finitely generated module,
integral extension,
Krull dimension,
KrullAkizuki Theorem,
Noetherian integral domain
Article copyright:
© Copyright 1974
American Mathematical Society
