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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
##### Keywords:
intersection property; avoidance principle
Full Text:
##### 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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