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

Modulus (algebraic Number Theory) - Definition

... Let K be a global

... 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

... 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

... 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

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

“Wynken and Blynken are two little eyes,

And Nod is a little head,

And the wooden shoe that sailed the skies

Is a wee one’s trundle-bed.”

—Eugene *Field* (1850–1895)

“Today, almost forty years later, I grow dizzy when I recall that the *number* of manufactured tanks seems to have been more important to me than the vanished victims of racism.”

—Albert Speer (1905–1981)

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