Remark on Rees valuations of finitely supported complete monomial ideals in a regular local ring

Abstract

Let be an equicharacteristic regular local ring of dimension and and consider the sequence of d-dimensional local monomial quadratic transformations where is a local monomial quadratic transformation of Ri for We prove that where and is the special -simple complete ideal associated with Let I and J be finitely supported complete -primary monomial ideals in R. We show that if the set of base points of the ideal IJ is linearly ordered, then