Algebraic extension

2020 Mathematics Subject Classification: Primary: 12F [MSN][ZBL]

A field extension $K/k$ in which every element of $K$ is algebraic over $k$; that is, every element of $K$ is the root of a polynomial with coefficients in $k$. A finite degree extension is necessarily algebraic, but the converse does not hold: for example, the field of algebraic numbers, the algebraic closure of the field of rational numbers, is an algebraic extension but not of finite degree.

References

[b1]	Paul J. McCarthy, "Algebraic Extensions of Fields", Courier Dover Publications (2014) ISBN 048678147X