Kaplansky/Nagata-type theorems for the half factorial domains

We give Kaplansky/Nagata-type theorems for the half factorial domains inside the class of atomic domains.Comment: 6 page

A locally F-finite Noetherian domain that is not F-finite

Using an old example of Nagata, we construct a Noetherian ring of prime characteristic p, whose Frobenius morphism is locally finite, but not finite.Comment: Comments are welcome