What is Field extension?
A '''field extension''' <math>K</math> is a [[Field (mathematics)|field]] containing a given field <math>k</math> as a [[subfield]].<ref>{{Cite web|title=Extension of a field - Encyclopedia of Mathematics|url=https://encyclopediaofmath.org/index.php?title=Extension_of_a_field|access-date=2021-09-15|website=encyclopediaofmath.org}}</ref> The notation <math>K/k</math> means that <math>K</math> is an extension of the field <math>k</math>. <math>K</math> is sometimes called an overfield of the field <math>k</math>. == Algebraic over <math>k</math> == An element of the field <math>K</math> is called algebraic over <math>k</math> if it satisfies some algebraic equation with coefficients in <math>k</math>, and transcendental otherwise. == References == <references /> [[Category:Algebraic number theory]]