Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Intersections of quasi-local domains

Author: Bruce Prekowitz
Journal: Trans. Amer. Math. Soc. 181 (1973), 329-339
MSC: Primary 13H10
MathSciNet review: 0319986
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Abstract: Let $ R = \bigcap {{V_i}} $ be an intersection of quasi-local domains with a common quotient field $ K$. Our goal is to find conditions on the $ {V_i}$'s in order to get some or all of $ {V_i}$'s to be localizations of $ R$. We show for example that if $ {V_1}$ is a $ 1$-dimensional valuation domain and if $ {V_1} \nsupseteq {V_2}$, then both $ {V_1}$ and $ {V_2}$ are localizations of $ R = {V_1} \cap {V_2}$.

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Keywords: Intersection, localization, quasi-local domains, valuation domains
Article copyright: © Copyright 1973 American Mathematical Society