primitive element


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primitive element

[′prim·əd·iv ′el·ə·mənt]
(mathematics)
A member of a finite number field from which all the other members can be generated by repeated multiplication.
References in classic literature ?
Who ever saw his old clothes -- his old coat, actually worn out, resolved into its primitive elements, so that it was not a deed of charity to bestow it on some poor boy, by him perchance to be bestowed on some poorer still, or shall we say richer, who could do with less?
After the nascent cosmos cooled a little, electrons and protons teamed up to form hydrogen, the most primitive element, and for hundreds of millions of years, this gas filled the universe.
For the typical primitive element of type X of dimension k we denote by [v.
To generate the non-zero elements of a finite field, we perform repeated exponentiations on the primitive element a until all the non-zero elements are generated.
From this point of view, the diatonic scale in the twenty-tone system is based on the automorphism generated by the primitive element 11, the "circle of sevenths," it turns out, and it has eleven elements.
If A is a Hopf algebra with comultiplication [gamma], then an element [rho] of A is called a primitive element if [gamma]([rho]) = [rho] [cross product] 1 + 1 [cross product] [rho].
Most inspiration ideas come from primitive elements, such as pets, fashion brands or origins.
Whatever they mean to Lee, the artist is clearly in touch with the most primitive elements of the psyche.
This trend has been marked in the case of imagery flowing from tribal and lower-caste practices into the classical tradition of Hinduism, whereas that of primitive elements amalgamating themselves into the Christian tradition was so far practically uncharted and unresearched territory.
Two artists in particular were axiomatic in promoting interest in the primitive: Paul Gauguin (1848-1903), who introduced Europeans to the culture of far-off peoples, and Pablo Picasso (1881-1973), who from around 1906 began to incorporate so-called primitive elements in his work.
The 22 papers, include discussions of one-particle irreducibility with initial correlations, primitive elements in the Hopf algebra of free quasi-symmetric functions, Magnus expansions and beyond, not so non-renormalizable gravity, a combinatorial and field theory path to quantum gravity, and multi-scale analysis and non-commutative field theory.
Observe that V is the set of primitive elements of C(V).