algebraic extension in a sentence
1) Separable extensions occur quite naturally within arbitrary algebraic field extensions .
algebraic collocations
2) It follows __FORMULA__ is an algebraic field extension of __FORMULA__.
3) If __FORMULA__ is an algebraic extension , then the following are equivalent.
algebraic extension example sentences
4) The fundamental theorem of Galois theory provides a link between algebraic field extensions and group theory.5) The aim of Galois theory is the study of " algebraic extensions " of a field.
6) From coefficients in an algebraic extension to coefficients in the ground field (see below).
7) It is thus necessary to have a notion of Galois group for an infinite algebraic extension .
8) Extended Euclidean algorithm is also the main tool for computing multiplicative inverses in simple algebraic field extensions .
9) An important application of extended GCD algorithm is that it allows to compute division in algebraic field extensions .
10) Every algebraic extension of the real field is isomorphic either to the real field or to the complex field.
11) There are other equivalent definitions of the notion of a separable algebraic extension , and these are outlined later in the article.
12) The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.
13) Since algebraic extensions of fields of characteristic zero, and of finite fields, are separable, separability is not an obstacle in most applications of Galois theory.
14) By contrast, the algebraic closure of __FORMULA__, denoted __FORMULA__, has infinite degree, i.e. __FORMULA__ has infinitely many inequivalent algebraic extensions .
15) Finite fields are used in number theory, Galois theory, coding theory and combinatorics; and again the notion of algebraic extension is an important tool.
example sentences with algebraic extension
16) The fundamental theorem of Galois theory shows that there is a strong relation between the structure of the symmetry group and the set of algebraic extensions .17) Galois theory aims to study the algebraic extensions of a field by studying the symmetry in the arithmetic operations of addition and multiplication.
18) Factoring over algebraic extensions (Trager's method)
19) __FORMULA__ has only a single proper algebraic extension : __FORMULA__; in other words, this quadratic extension is already algebraically closed.
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