primitive element

名词 n.

中文释义

英文释义

名词 n.

An element that generates a simple extension.

— An algebraic extension L#47;K is called simple if L#61;K(#92;alpha) for some #92;alpha#92;inL. The element #92;alpha is called a primitive element for L#47;K. Every finite separable algebraic field extension is simple. Suppose that L#61;K(#92;alpha#95;1,#92;dots#92;alpha#95;r) is a finite separable extension and K#95;0#92;subseteqK is an infinite subset of K. Then there exists a primitive element #92;alpha of the form #92;textstyle#92;alpha#61;#92;sum#95;#123;i#61;1#125;ʳc#95;i#92;alpha#95;i with c#95;i#92;inK#95;0.
An element that generates the multiplicative group of a given Galois field (finite field).

— Furthermore, if the irreducible polynomial has a primitive element α (where α=1) that is a root, then the polynomial is termed a primitive polynomial and corresponds to the polynomial for a maximal length feedback shift register.
Given a modulus n, a number g such that every number coprime to n is congruent (modulo n) to some power of g; equivalently, a generator of the multiplicative field of integers modulo n.

— Let A be a prime number for which 2 is a primitive element. Then 2#123;A-1#125;-1 is divisible by A.
An element that is not a positive integer multiple of another element of the lattice.

— But suppose L'#92;inC#95;#92;nu(S#95;0) so that #92;operatorname#123;det#125;(L')#61;#92;eta'#92;pi#92;blacktriangleright 0 for some totally positive unit #92;eta' and so that L' is everywhere locally a primitive''' element of the #92;mathfrako-lattice R#95;#92;nu.
An element x ∈ C such that μ(x) = x ⊗ g + g ⊗ x, where μ is the comultiplication and g is an element that maps to the multiplicative identity 1 of the base field under the counit (in particular, if C is a bialgebra, g = 1).

— 2009, Masoud Khalkhali, Basic Noncommutative Geometry, European Mathematical Society, page 29, A primitive element of a Hopf algebra is an element h∈H such that Δh=1⊗h+h⊗1. It is easily seen that the bracket [x,y]:=xy-yx of two primitive elements is again a primitive element. It follows that primitive elements form a Lie algebra. For H=U(g) any element of g is primitive and in fact using the Poincaré-Birkhoff-Win theorem, one can show that the set of primitive elements of U(g) coincides with the Lie algebra g.
An element of a free generating set of a given free group.

— In this paper we apply regression models and other pattern recognition techniques to the task of classifying primitive elements of a free group.

词形变化

primitive elements plural

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近义词

primitive root