Let B be a ring with a subring A. An element xB is algebraic over A if there exist elements a1,,anA, with an0, such that


An element xB 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