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:
“... the first reason for psychology’s failure to understand what people are and how they act, is that clinicians and psychiatrists, who are generally the theoreticians on these matters, have essentially made up myths without any evidence to support them; the second reason for psychology’s failure is that personality theory has looked for inner traits when it should have been looking for social context.”
—Naomi Weisstein (b. 1939)