Definition:Algebraic Element of Ring Extension

Definition
Let $\struct {R, +, \circ}$ be a commutative ring with unity whose zero is $0_R$ and whose unity is $1_R$.

Let $\struct {D, +, \circ}$ be an integral subdomain of $R$.

Let $x \in R$.

Then $x$ is algebraic over $D$ :
 * $\exists \map f x$ over $D$ such that $\map f x = 0_R$

where $\map f x$ is a non-null polynomial in $x$ over $D$.

Also see

 * An element of $R$ is said to be transcendental if it is not algebraic.


 * Definition:Integral Element of Ring Extension