This tag is for questions regarding to the Integral Extensions or, Integral Ring Extensions.
Let $~A ⊆ B~$ be a ring extension. Generalizing to rings the notion of algebraic elements and extensions from field theory, we say that an element $~b~$ in $~B~$ is integral over $~A~$ if there exists a monic polynomial $~f(x)~$ in the variable $~x~$ with coefficients in $~A~$ such that $~f(b) = 0~$; we say that the extension is integral if every element of $~B~$ is integral over $~A~$.
- A domain that is an integral extension of a field must be a field
Reference:
https://en.wikipedia.org/wiki/Integral_element#Integral_extensions
"Integral Extensions" by Siegfried Bosch