Definition of Subextension. Meaning of Subextension. Synonyms of Subextension

- F} is said to be an intermediate field (or intermediate extension or subextension) of L / K {\displaystyle L/K} . Given a field extension L / K {\displaystyle...
- either an extension formed by adjoining roots of unity to a field, or a subextension of such an extension. The cyclotomic fields are examples. A cyclotomic...
- (Intermediate fields are fields K satisfying F ⊆ K ⊆ E; they are also called subextensions of E/F.) For finite extensions, the correspondence can be described...
- containing all (algebraic) separable extensions of K within Kalg. This subextension is called a separable closure of K. Since a separable extension of a...
- {D}}_{L/K}} of the extension L / K {\displaystyle L/K} and that of subextensions: w ( D L / K ) = ∑ s ≠ 1 i G ( s ) = ∑ i = 0 ∞ ( | G i | − 1 ) . {\displaystyle...
- is odd. By the fundamental theorem of Galois theory, there exists a subextension L of K/R such that Gal(K/L) = H. As [L:R] = [G:H] is odd, and there are...
- Galois if and only if E {\displaystyle E} is the union of finite Galois subextensions E i / F {\displaystyle E_{i}/F} indexed by an (infinite) index set I...
- not finitely generated is called separable if every finitely generated subextension has a separating transcendence basis. Let E ⊇ F {\displaystyle E\supseteq...
- correspondence establishes a one to one correspondence between the subextensions of a normal field extension F / E {\displaystyle F/E} and the subgroups...
- Lüroth solved in the nineteenth century. Lüroth's problem concerns subextensions L of K(X), the rational functions in the single indeterminate X. Any...