Construction and finite generation of the strict closure of rings

Abstract

The construction of Arf rings and strictly closed rings has been studied widely; however, there has been no clear description of the structure of the strict closure R^* when the integral closure of R is not a finitely generated R-module. In this paper, we investigate the construction and finite generation of the strict closure of rings. We determine its structure when R is a Cohen-Macaulay semi-local ring of dimension one, with dim R_M=1 for every Maximal ideal M in R. Using this, a characterization of the finite generation of the strict closure is given.