Meaning of field extension | Babel Free

Definitions

Any pair of fields, denoted L/K, such that K is a subfield of L.

Equivalents

Examples

“A Galois field extension may be defined in terms of its Galois group (Section 2) or in terms of the internal structure⟳ of the extension (Section 3).”

“1998, David Goss, Basic Structures of Function Field Arithmetic, Springer, Corrected 2nd Printing, page 283, Note⟳ that the extension of L obtained by adjoining all division points of ψ includes at most a finite constant field extension.”

“2007, Pierre Antoine Grillet, Abstract Algebra, Springer, 2bd Edition, page 530, A field extension of a field K is, in particular, a K-algebra. Hence any two field extensions of K have⟳ a tensor product that is a K-algebra.”

CEFR level