Algebraic extension
FIELD EXTENSION VIA ADJOINING SOLUTIONS TO POLYNOMIALS WITH COEFFICIENTS IN THE SUBFIELD
Algebraic extension of a field; Algebraic field extension; Relative algebraic closure; Algebraic extension field
In mathematics, an algebraic extension is a field extension such that every element of the larger field is algebraic over the smaller field ; that is, if every element of is a root of a non-zero polynomial with coefficients in .Fraleigh (2014), Definition 31.