Galois Theory
- Galois extension
- A normal, separable field extension.
- Galois group
- The automorphism group of a Galois extension. When it is a finite extension, this is a finite group of order equal to the degree of the extension. Galois groups for infinite extensions are profinite groups.
- Kummer theory
- The Galois theory of taking n-th roots, given enough roots of unity. It includes the general theory of quadratic extensions.
- Artin-Schreier theory
- Covers an exceptional case of Kummer theory, in characteristic p.
- Normal basis
- A basis in the vector space sense of L over K, on which the Galois group of L over K acts transitively.
- Tensor product of fields
- A different foundational piece of algebra, including the compositum operation (join of fields).
Read more about this topic: Glossary Of Field Theory
Famous quotes containing the word theory:
“Don’t confuse hypothesis and theory. The former is a possible explanation; the latter, the correct one. The establishment of theory is the very purpose of science.”
—Martin H. Fischer (1879–1962)