Independent locally-finite intersections of localizations (Q2705864)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Independent locally-finite intersections of localizations |
scientific article |
Statements
19 March 2001
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Matlis \(k\)-local domains
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Krull rings
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Ribenboim generalized Krull domains
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integral domain
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0.88832635
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0.8820044
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0.8805119
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0.8801822
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0.8799545
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Independent locally-finite intersections of localizations (English)
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Let \(D\) be an integral domain and \(\mathcal F\) a set of prime ideals of \(D\). Here are studied rings \(D\) such that \(D=\bigcap_{p\in{\mathcal F}}D_p\), every non-zero non-unit of \(D\) belongs to at most finitely many primes of \(\mathcal F\) and for \(p,q\in{\mathcal F}\) there is no non-zero prime ideal contained in \(p\cap q\). Examples of such rings include Noetherian domains in which grade-one primes have height one, rings of Krull type and the so-called \(h\)-local domains of \textit{E. Matlis} [``Torsion-free modules'', Chicago Lect. Math. Chicago-London (1972; Zbl 0298.13001)].
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