plural of Extension Scout

(Scouting) A youth member of the Extension Scouting program.

(algebra, field theory, algebraic geometry) Any pair of fields, denoted L/K, such that K is a subfield of L.

(algebra, field theory) A field extension L/K which is algebraic over K (i.e., is such that every element of L is a root of some (nonzero) polynomial with coefficients in K).

(algebra, Galois theory) An algebraic extension that is both a normal and a separable extension; equivalently, an algebraic extension E/F such that the fixed field of its automorphism group (Galois group) Aut(E/F) is the base field F.

Alternative form of underextension.

Alternative form of overextension.

(algebra, field theory) A field extension obtained by adjoining a single element to a given field.

(algebra) A finite (and thereby algebraic) extension of a base field such that every element of the extension is the root of a separable polynomial over the base field.

(algebra) A finite, algebraic extension of some field such that if it contains any root of any irreducible polynomial over that base field then it contains all of the roots of that polynomial.