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An algebraic variety over a field K that becomes isomorphic to a projective space.

For a Galois extension field K of a field F, the fundamental theorem of Galois theory states that the subgroups of the Galois group G=Gal(K/F) correspond with the subfields ...

The multiplicative subgroup of all elements in the product of the multiplicative groups k_nu^× whose absolute value is 1 at all but finitely many nu, where k is a number ...

A function A such that B=del xA. The most common use of a vector potential is the representation of a magnetic field. If a vector field has zero divergence, it may be ...

An algorithm for determining the order of an elliptic curve E/F_p over the finite field F_p.

An extension F of a field K is said to be algebraic if every element of F is algebraic over K (i.e., is the root of a nonzero polynomial with coefficients in K).

The pure equation x^p=C of prime degree p is irreducible over a field when C is a number of the field but not the pth power of an element of the field. Jeffreys and Jeffreys ...

A subfield which is strictly smaller than the field in which it is contained. The field of rationals Q is a proper subfield of the field of real numbers R which, in turn, is ...

A polynomial p(x)=sumc_ix^i is said to split over a field K if p(x)=aproduct_(i)(x-alpha_i) where a and alpha_i are in K. Then the polynomial is said to split into linear ...

An algebraic extension K over a field F is a purely inseparable extension if the algebraic number minimal polynomial of any element has only one root, possibly with ...