finite field

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• Finite field — In abstract algebra, a finite field or Galois field (so named in honor of Évariste Galois) is a field that contains only finitely many elements. Finite fields are important in number theory, algebraic geometry, Galois theory, cryptography, and… …   Wikipedia

• Finite field arithmetic — Arithmetic in a finite field is different from standard integer arithmetic. There are a limited number of elements in the finite field; all operations performed in the finite field result in an element within that field.While each finite field is …   Wikipedia

• Quasi-finite field — In mathematics, a quasi finite field is a generalisation of a finite field. Standard local class field theory usually deals with complete fields whose residue field is finite , but the theory applies equally well when the residue field is only… …   Wikipedia

• Block Lanczos algorithm for nullspace of a matrix over a finite field — The Block Lanczos algorithm for nullspace of a matrix over a finite field is a procedure for finding the nullspace of a matrix using only multiplication of the matrix by long, thin matrices. These long, thin matrices are considered as vectors of… …   Wikipedia

• Primitive element (finite field) — In field theory, a branch of mathematics, a primitive element of a finite field GF ( q ) is a generator of the multiplicative group of the field, which is necessarily cyclic. The minimal polynomial of a primitive element is a primitive polynomial …   Wikipedia

• Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …   Wikipedia

• Field extension — In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… …   Wikipedia

• Field arithmetic — In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a ql|field (mathematics)|field and its absolute Galois group.It is an interdisciplinary subject as it uses tools from algebraic number… …   Wikipedia

• Finite group — In mathematics, a finite group is a group which has finitely many elements. Some aspects of the theory of finite groups were investigated in great depth in the twentieth century, in particular the local theory, and the theory of solvable groups… …   Wikipedia

• Field with one element — In mathematics, the field with one element is a suggestive name for an object that should exist: many objects in math have properties analogous to objects over a field with q elements, where q = 1, and the analogy between number fields and… …   Wikipedia

• Field of definition — In mathematics, the field of definition of an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining V can belong. Given polynomials, with coefficients in a field K , it may not be obvious… …   Wikipedia