In field theory, a branch of
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External links
*MathWorld | title=Primitive Polynomial | urlname=PrimitivePolynomial
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Primitive element theorem — In mathematics, more specifically in field theory, the primitive element theorem provides a characterization of the finite field extensions which are simple and thus can be generated by the adjunction of a single primitive element. Primitive… … Wikipedia
Primitive element — In mathematics, the term primitive element can mean: * Primitive root modulo n , in number theory * Primitive element (field theory), an element that generates a given field extension * Primitive element (finite field), an element that generates… … 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
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
Primitive — is a subjective label used to imply that one thing is less sophisticated or less advanced than some other thing. Being a comparative word it is also relative in nature.Indigenous peoples and their beliefs and practices are sometimes described as… … Wikipedia
Primitive permutation group — In mathematics, a permutation group G acting on a set X is called primitive if G preserves no nontrivial partition of X . In the other case, G is imprimitive. An imprimitive permutation group is an example of an induced representation; examples… … 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 (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
Primitive polynomial — In field theory, a branch of mathematics, a primitive polynomial is the minimal polynomial of a primitive element of the finite extension field GF( p m ). In other words, a polynomial F(X) with coefficients in GF( p ) = Z/ p Z is a primitive… … Wikipedia
Glossary of field theory — Field theory is the branch of mathematics in which fields are studied. This is a glossary of some terms of the subject. (See field theory (physics) for the unrelated field theories in physics.) Definition of a field A field is a commutative ring… … Wikipedia
