Answer to Question #24418 in Algebra for siavosh

Question

If U is a multiplicatively closed subset of R contained by T and M is an integrally closed
R-module , then U^(-1)M is integrally closed over both R and U^(-1) R .

Answer 1

Statement is true as propertybeing integrally closed means to be equal to integral closure, and as S is in the R, and M - is integrally closed and then localization preservers
it, and more over U^(-1) R.