# Number Field

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

Lattice Sieving
... It 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 ...
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 ... 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 ... that all maximal subfields of a division algebra D are splitting fields ...
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 ...
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 ...

### Famous quotes containing the words field and/or number:

Frankly, I’d like to see the government get out of war altogether and leave the whole field to private industry.
Joseph Heller (b. 1923)

As equality increases, so does the number of people struggling for predominance.
Mason Cooley (b. 1927)