Czechoslovak Mathematical Journal, Vol. 70, No. 4, pp. 1191-1196, 2020

Avoidance principle and intersection property for a class of rings

Rahul Kumar, Atul Gaur

Received August 8, 2019.   Published online April 16, 2020.

Abstract:  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.
Keywords:  intersection property; avoidance principle
Classification MSC:  13A99, 13B30
DOI:  10.21136/CMJ.2020.0360-19

[1] C. Gottlieb: Finite unions of overrings of an integral domain. (to appear) in J. Commut. Algebra Available at
[2] W. W. Smith: 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

Affiliations:   Rahul Kumar, Atul Gaur (corresponding author), Department of Mathematics, University of Delhi, New Academic Block, University Enclave, Delhi, 110007, India, e-mail:,

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