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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 ...

A quadratic form involving n real variables x_1, x_2, ..., x_n associated with the n×n matrix A=a_(ij) is given by Q(x_1,x_2,...,x_n)=a_(ij)x_ix_j, (1) where Einstein ...

The concept of a space is an extremely general and important mathematical construct. Members of the space obey certain addition properties. Spaces which have been ...

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

Differential algebra is a field of mathematics that attempts to use methods from abstract algebra to study solutions of systems of polynomial nonlinear ordinary and partial ...

A vector basis of a vector space V is defined as a subset v_1,...,v_n of vectors in V that are linearly independent and span V. Consequently, if (v_1,v_2,...,v_n) is a list ...

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).