Sentence examples for field extensions from inspiring English sources

Discriminants also are defined for elliptic curves, finite field extensions, quadratic forms, and other mathematical entities.

This work is intended to analyse the hardware possibilities of the algorithms performing multiplication in finite field extensions GF 2m).

It turned from the study of substitutions in formulas and of functions invariant under such substitutions into the study of field extensions and corresponding automorphisms (Stein 1988, earlier Mehrtens 1979b).

Since all finite connected étale coverings of R n are also Laurent polynomial rings over field extensions of k [19, lemma 2.8] and the statement is stable under products, the theorem also holds for induced tori.

Galois groups of infinite field extensions such as the absolute Galois group can also be equipped with a topology, the so-called Krull topology, which in turn is central to generalize the above sketched connection of fields and groups to infinite field extensions.

More generally, field extensions provide another class of examples of vector spaces, particularly in algebra and algebraic number theory: a field containing a smaller field is an -vector space, by the given multiplication and addition operations of.

We also discuss the far field extension of this concept.

There are two basic types of de-interlacing algorithms: field combination and field extension [15].

Similarly if we replace R x by K or any field extension of K.  .

The behaviour under a given tamely ramified finite Galois field extension L / K is subtle.

In the field extension type, there is a de-interlacing method called vertical half-sizing.