algebraic
Let B be a ring with a subring A. An element x∈B is algebraic over A if there exist elements a1,…,an∈A, with an≠0, such that
anxn+an-1xn-1+⋯+a1x+a0=0. |
An element x∈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 |
---|---|
Canonical name | Algebraic1 |
Date of creation | 2013-03-22 12:07:50 |
Last modified on | 2013-03-22 12:07:50 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 8 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 13B02 |
Related topic | AlgebraicExtension |
Defines | transcendental |