On the ubiquity of arf rings

We introduce and develop the theory of weakly Arf rings, generalizing the Arf rings originally defined by J. Lipman in 1971. We provide characterizations of the weakly Arf rings and study their relation with the Arf rings and the strictly closed rings. Furthermore, we give various examples of weakly Arf rings that come from idealizations, fiber products, determinantal rings, and invariant subrings.