# integral closure

Let $B$ be a ring with a subring $A$. The of $A$ in $B$ is the set $A^{\prime}\subset B$ consisting of all elements of $B$ which are integral over $A$.

It is a theorem that the integral closure of $A$ in $B$ is itself a ring. In the special case where $A=\mathbb{Z}$, the integral closure $A^{\prime}$ of $\mathbb{Z}$ is often called the ring of integers in $B$.

Title integral closure IntegralClosure 2013-03-22 12:07:53 2013-03-22 12:07:53 djao (24) djao (24) 8 djao (24) Definition msc 13B22 IntegrallyClosed ring of integers