# integral

Let $B$ be a ring with a subring $A$. We will assume that $A$ is contained in the center of $B$ (in particular, $A$ is commutative). An element $x\in B$ is integral over $A$ if there exist elements $a_{0},\dots,a_{n-1}\in A$ such that

 $x^{n}+a_{n-1}x^{n-1}+\cdots+a_{1}x+a_{0}=0.$

The ring $B$ is integral over $A$ if every element of $B$ is integral over $A$.

Title integral Integral 2013-03-22 12:07:44 2013-03-22 12:07:44 djao (24) djao (24) 9 djao (24) Definition msc 13B21 IntegralBasis