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Avoidance principle and intersection property for a class of rings. (English) Zbl 07285990
Summary: Let \(R\) be a commutative ring with identity. If a ring \(R\) is contained in an arbitrary union of rings, then \(R\) is contained in one of them under various conditions. Similarly, if an arbitrary intersection of rings is contained in \(R\), then \(R\) contains one of them under various conditions.
MSC:
13A99 General commutative ring theory
13B30 Rings of fractions and localization for commutative rings
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References:
[1] Gottlieb, C., Finite unions of overrings of an integral domain, (to appear) in J. Commut. Algebra Available at https://projecteuclid.org/euclid.jca/1543654843
[2] Smith, W. W., A covering condition for prime ideals, Proc. Am. Math. Soc. 30 (1971), 451-452
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