prove that every root closed domain is integrally closed
I want to help but I am not sure what you mean by "root closed domain" and by "integrally closed domain". Here is my understanding, if is a subsring of a domain and is root closed, i.e. every element in is a zero of some (monic?) polynomial. Then it is integrally closed meaning if then it is zero of some (monic?) polynomial in . Right or wrong?