prove that everyroot closed domainis integrally closed

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- Nov 23rd 2007, 10:28 AMsehrishqauintegrally closed domain
prove that every

**root closed domain**is integrally closed - Nov 23rd 2007, 11:51 AMThePerfectHacker
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 $\displaystyle R$ is a subsring of a domain $\displaystyle D$ and $\displaystyle R$ is root closed, i.e. every element in $\displaystyle R$ is a zero of some (monic?) polynomial. Then it is integrally closed meaning if $\displaystyle d\in D$ then it is zero of some (monic?) polynomial in $\displaystyle R$. Right or wrong?