An element $s \in S$ is integral over $R$ if there exists a monic polynomial $P(x) \in R[x]$ such that $P^\varphi (s) = 0$, where $P^\varphi (x) \in S[x]$ is the image of $P$ under $\varphi : R[x] \to S[x]$.
The ring map $\varphi $ is integral if every $s \in S$ is integral over $R$.
Post a comment
Your email address will not be published. Required fields are marked.
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).