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intersection property; avoidance principle
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.
[1] Gottlieb, C.: Finite unions of overrings of an integral domain. (to appear) in J. Commut. Algebra Available at
[2] Smith, W. W.: A covering condition for prime ideals. Proc. Am. Math. Soc. 30 (1971), 451-452. DOI 10.1090/S0002-9939-1971-0282963-2 | MR 0282963 | Zbl 0219.13004
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