# Number Field

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

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 case, where ...
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 ... a local-global theorem stating that if a finite dimensional central division algebra over a number field splits locally everywhere then it splits globally (so is ... theorems allow one to classify all finite dimensional central division algebras over a given number field ...
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
... It is almost exclusively used in conjunction with the number field sieve ... implicitly involves the ideal structure of the number field of the polynomial it takes advantage of the theorem that any prime ideal above some ... 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 ...

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

An enormously vast field lies between “God exists” and “there is no God.” The truly wise man traverses it with great difficulty. A Russian knows one or the other of these two extremes, but is not interested in the middle ground. He usually knows nothing, or very little.
Anton Pavlovich Chekhov (1860–1904)

It seems to me that there must be an ecological limit to the number of paper pushers the earth can sustain, and that human civilization will collapse when the number of, say, tax lawyers exceeds the world’s total population of farmers, weavers, fisherpersons, and pediatric nurses.
Barbara Ehrenreich (b. 1941)