Abstract
A ring R will be called dagger if holds in R. We will show that any 2-integrally closed domain is dagger, and that, when the characteristic is not two, a 2-root closed and dagger domain is 2-integrally closed. Examples and non-examples of dagger domains are constructed.
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Acknowledgements
The author would like to thank Muhammad Zafrullah for his insightful comments and suggestions.