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Primitive Mentality
Primitive may refer to: Mathematics * Primitive element (field theory) * Primitive element (finite field) * Primitive cell (crystallography) * Primitive notion, axiomatic systems * Primitive polynomial (other), one of two concepts * Primitive function or antiderivative, ''F''′ = ''f'' * Primitive permutation group * Primitive root of unity; See Root of unity#General definition, Root of unity * Primitive triangle, an integer triangle whose sides have no common prime factor Sciences * Primitive (phylogenetics), characteristic of an early stage of development or evolution * Primitive equations, a set of nonlinear differential equations that are used to approximate atmospheric flow * Primitive change, a general term encompassing a number of basic molecular alterations in the course of a chemical reaction Computing * Cryptographic primitives, low-level cryptographic algorithms frequently used to build computer security systems * Geometric primitive, the simplest kinds of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Primitive Element (field Theory)
In field theory, a simple extension is a field extension which is generated by the adjunction of a single element. Simple extensions are well understood and can be completely classified. The primitive element theorem provides a characterization of the finite simple extensions. Definition A field extension is called a simple extension if there exists an element in ''L'' with :L = K(\theta). This means that every element of can be expressed as a rational fraction in , with coefficients in . There are two different sort of simple extensions. The element may be transcendental over , which means that it is not a root of any polynomial with coefficients in . In this case K(\theta) is isomorphic to the field of rational functions K(X). Otherwise, is algebraic over ; that is, is a root of a polynomial over . The monic polynomial F(X) of minimal degree , with as a root, is called the minimal polynomial of . Its degree equals the degree of the field extension, that is, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |