cyclotomic rational

См. также в других словарях:

• Cyclotomic field — In number theory, a cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to Q, the field of rational numbers. The n th cyclotomic field Q(ζn) (with n > 2) is obtained by adjoining a primitive n… …   Wikipedia

• Cyclotomic character — In number theory, a cyclotomic character is a character of a Galois group giving the Galois action on a group of roots of unity. As a one dimensional representation over a ring R, its representation space is generally denoted by R(1) (that is, it …   Wikipedia

• Gaussian rational — In mathematics, a Gaussian rational number is a complex number of the form p + qi, where p and q are both rational numbers. The set of all Gaussian rationals forms the Gaussian rational field, denoted Q(i), obtained by adjoining the… …   Wikipedia

• Root of unity — The 5th roots of unity in the complex plane In mathematics, a root of unity, or de Moivre number, is any complex number that equals 1 when raised to some integer power n. Roots of unity are used in many branches of mathematics, and are especially …   Wikipedia

• Inverse Galois problem — In mathematics, the inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of the rational numbers Q. This problem, first posed in the 19th centuryFact|date=February 2007, is… …   Wikipedia

• Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

• p-adic number — In mathematics, and chiefly number theory, the p adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number… …   Wikipedia

• P-adic number — In mathematics, the p adic number systems were first described by Kurt Hensel in 1897 [cite journal | last = Hensel | first = Kurt | title = Über eine neue Begründung der Theorie der algebraischen Zahlen | journal =… …   Wikipedia

• Cubic field — In mathematics, specifically the area of algebraic number theory, a cubic field is an algebraic number field of degree three. Contents 1 Definition 2 Examples 3 Galois closure 4 …   Wikipedia

• Bernoulli number — In mathematics, the Bernoulli numbers Bn are a sequence of rational numbers with deep connections to number theory. They are closely related to the values of the Riemann zeta function at negative integers. There are several conventions for… …   Wikipedia

• Algebraically closed field — In mathematics, a field F is said to be algebraically closed if every polynomial in one variable of degree at least 1, with coefficients in F , has a root in F . ExamplesAs an example, the field of real numbers is not algebraically closed,… …   Wikipedia