A special subring of the Nagata ring and the Serre's conjecture ring

Many ring theorists researched various properties of Nagata rings and Serre’s conjecture rings. In this paper, we introduce a subring (refer to the Anderson ring) of both the Nagata ring and the Serre’s conjecture ring (up to isomorphism), and investigate properties of the Anderson ring. Additionally, we compare the properties of the Anderson ring with those of the Nagata ring and the Serre’s conjecture ring.