show · ring.integral all knowls · up · search:

If $R\subseteq S$ are commutative rings with one, an element $s\in S$ is integral over $R$ if there exists $n\in\Z^+$ and $a_i\in R$ such that $$ s^n+a_{n-1} s^{n-1}+\cdots + a_0 =0\,.$$

The integral closure of $R$ in $S$ is $\{s\in S\mid s \text{ is integral over } R\}$.

Authors:
Knowl status:
  • Review status: reviewed
  • Last edited by John Jones on 2018-08-06 14:56:01
Referred to by:
History: (expand/hide all)