  We introduce and develop the theory of weakly Arf rings, which is a
generalization of Arf rings, initially defined by J. Lipman in 1971. We provide
characterizations of weakly Arf rings and study the relation between these
rings, the Arf rings, and the strict closedness of rings. Furthermore, we give
various examples of weakly Arf rings that come from idealizations, fiber
products, determinantal rings, and invariant subrings.
