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The Einstein field equations are the 16 coupled hyperbolic-elliptic nonlinear partial differential equations that describe the gravitational effects produced by a given mass ...

A map f:R^n|->R which assigns each x a scalar function f(x).

An extremely fast factorization method developed by Pollard which was used to factor the RSA-130 number. This method is the most powerful known for factoring general numbers, ...

Gauge theory studies principal bundle connections, called gauge fields, on a principal bundle. These connections correspond to fields, in physics, such as an electromagnetic ...

If a subset S of the elements of a field F satisfies the field axioms with the same operations of F, then S is called a subfield of F. In a finite field of field order p^n, ...

An extension field of a field F that is not algebraic over F, i.e., an extension field that has at least one element that is transcendental over F. For example, the field of ...

A finite division algebra is a field.

The field of complex numbers, denoted C.

If a is an element of a field F over the prime field P, then the set of all rational functions of a with coefficients in P is a field derived from P by adjunction of a.

The prime subfield of a field F is the subfield of F generated by the multiplicative identity 1_F of F. It is isomorphic to either Q (if the field characteristic is 0), or ...