in this article, we study the artin-rees property in c(x), in the rings of fractions of c(x) and in the factor rings of c(x) . we show that c(x)/(f) is an artin-rees ring if and only if z(f) is an open p-space. a necessary and sufficient condition for the local rings of c(x) to be artin-rees rings is that each prime ideal in c(x) becomes minimal and it turns out that every local ring ...
