field extension
Noun
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.003
Noun
field extension (plural field extensions)
- (algebra, field theory, algebraic geometry) Any pair of field, denoted L/K, such that K is a subfield of L.
- 1974, Thomas W. Hungerford, Algebra, Springer, page 230 ↗,
- 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 \psi 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.
- 1974, Thomas W. Hungerford, Algebra, Springer, page 230 ↗,
This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.003