A generalization of Kronecker function rings and Nagata rings
  Despite the obvious similarities in definitions and properties, the Nagata ring and the Kronecker function ring have been classically treated independently, when the coefficients are not in a Pr\"ufer domain. The purpose of this paper is to study two different unified approaches to the Nagata rings and the Kronecker function rings, which yield these rings and their classical generalizations as special cases. 
Marco Fontana and K. Alan Loper