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Ascending chain conditions and star operations. (English) Zbl 0691.13013

Conditions are given for an integral domain with a star operation * to have ascending chain condition on *-ideals. This is used to give some conditions under which a Mori domain is a Krull domain. It is shown that an integral domain is a Krull domain if and only if it has a star operation * for which every nonzero fractional ideal is *-invertible. A new class of rings called pre-Krull domains is discussed briefly.
Reviewer: W.H.Gustafson

MSC:

13E99 Chain conditions, finiteness conditions in commutative ring theory
13A99 General commutative ring theory
13G05 Integral domains
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References:

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[8] DOI: 10.1007/BF01310053 · Zbl 0383.13013
[9] DOI: 10.1112/S0025579300011268 · Zbl 0613.13001
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