# algebraic

Let $B$ be a ring with a subring $A$. An element $x\in B$ is algebraic over $A$ if there exist elements $a_{1},\dots,a_{n}\in A$, with $a_{n}\neq 0$, such that

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

An element $x\in B$ is transcendental over $A$ if it is not algebraic.

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

Title algebraic Algebraic1 2013-03-22 12:07:50 2013-03-22 12:07:50 djao (24) djao (24) 8 djao (24) Definition msc 13B02 AlgebraicExtension transcendental