# integrally closed domain

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 $R$ is a subsring of a domain $D$ and $R$ is root closed, i.e. every element in $R$ is a zero of some (monic?) polynomial. Then it is integrally closed meaning if $d\in D$ then it is zero of some (monic?) polynomial in $R$. Right or wrong?