infinite extension

infinite extension

[′in·fi·nit ik′sten·chən]
(mathematics)
An extension field F of a given field E such that F, viewed as a vector space over E, has infinite dimension.
References in periodicals archive ?
The Kingdom of Saudi Arabia is of the view that it is imperative that the states do not experience any doubts or concerns about the wisdom of accepting an infinite extension of the NPT treaty, or even the accession to it," he said.
Alice Ambrose), which Braver discusses on page 181: "We must not suppose that with the rule we have given the infinite extension of its application.
It conjures something else: infinite extension, scanning, even searching.
The placing seems unimportant too, for even if you stand with a printed piece of cloth with a quite specific demarcation, in principle it appears to have been taken out of the infinite extension of an ideal pattern.
This volume integral would be impossible without the boundary, because the linear solution, being alone, is not physically meaningful for the infinite extension.
For example, the infinite extension of a finite-dimensional control system leads to a system whose state space consists of all infinite sequences.
In theory, the desk is capable of infinite extension.
in the cast I saw, only Cohen, with her ability to dart into one movement and stretch the next one into an infinite extension, appeared to have the steely, clean qualities of a Balanchinian dancer.
Other revisions to this second edition include an earlier introduction to noncommutative rings; a simpler treatment of the existence of free groups; and new discussions of Galois theory for infinite extensions, the normal basis theory, abelian categories, and module categories.
The film begins in the middle of a movement and ends in the middle of a movement, suggesting the infinite extensions of a fugue rather than an enclosed climactic structure," Deren noted, adding: "The other problem which I began working on in this film is the relating of sound to images brought together from independent sources, rather than that the source of the sound and image be one and the same as in the theatrical tradition, which dominates most film.