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A field K is said to be an extension field (or field extension, or extension), denoted K/F, of a field F if F is a subfield of K. For example, the complex numbers are an ...

The degree (or relative degree, or index) of an extension field K/F, denoted [K:F], is the dimension of K as a vector space over F, i.e., [K:F]=dim_FK. If [K:F] is finite, ...

Given a field F and an extension field K superset= F, if alpha in K is an algebraic element over F, the minimal polynomial of alpha over F is the unique monic irreducible ...

Let X be a set of urelements, and let V(^*X) be an enlargement of the superstructure V(X). Let A in V(X) be a finitary algebra with finitely many fundamental operations. Then ...

Given a subspace A of a space X and a map from A to a space Y, is it possible to extend that map to a map from X to Y?

A extension ring (or ring extension) of a ring R is any ring S of which R is a subring. For example, the field of rational numbers Q and the ring of Gaussian integers Z[i] ...

The radius of the smallest circle centered at one of the points of an N-cluster, which contains all the points in the N-cluster.

That portion of a region lying "outside" a specified boundary.

Exterior algebra is the algebra of the wedge product, also called an alternating algebra or Grassmann algebra. The study of exterior algebra is also called Ausdehnungslehre ...

An exterior angle beta of a polygon is the angle formed externally between two adjacent sides. It is therefore equal to 2pi-alpha, where alpha is the corresponding internal ...