Number Field

Some articles on field, number field, numbers, number:

Modulus (algebraic Number Theory) - Definition
... Let K be a global field with ring of integers R ... If K is a number field, ν(p) = 0 or 1 for real places and ν(p) = 0 for complex places ... If K is a function field, ν(p) = 0 for all infinite places ...
Lattice Sieving
... is almost exclusively used in conjunction with the number field sieve ... The algorithm implicitly involves the ideal structure of the number field of the polynomial it takes advantage of the theorem that any prime ideal above some rational prime p can be written as ... One then picks many prime numbers q of an appropriate size, usually just above the factor base limit, and proceeds by For each q, list the prime ideals above q by factorising the polynomial f(a,b ...
Wieferich@Home - Properties - Connection With Fermat's Last Theorem
... K = Q(ξ) is the field extension obtained by adjoining all polynomials in the algebraic number ξ to the field of rational numbers (such an extension is known as a number field or in this particular ...
Emmy Noether - Contributions To Mathematics and Physics - Third Epoch (1927–35) - Noncommutative Algebra
... Noether also was responsible for a number of other advancements in the field of algebra ... if a finite dimensional central division algebra over a number field splits locally everywhere then it splits globally (so is trivial), and from this, deduced their Hauptsatz ("main theorem") every finite ... central division algebras over a given number field ...

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