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

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 case, where ...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 ... 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

... 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

... 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)

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