field discriminant

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• Discriminant — In algebra, the discriminant of a polynomial is an expression which gives information about the nature of the polynomial s roots. For example, the discriminant of the quadratic polynomial is Here, if Δ > 0, the polynomial has two real roots,… …   Wikipedia

• Discriminant of an algebraic number field — A fundamental domain of the ring of integers of the field K obtained from Q by adjoining a root of x3 − x2 − 2x + 1. This fundamental domain sits inside K ⊗QR. The discriminant of K is 49 = 72.… …   Wikipedia

• discriminant — discriminantal /dis krim euh nan tl/, adj. /di skrim euh neuhnt/, n. Math. a relatively simple expression that determines some of the properties, as the nature of the roots, of a given equation or function. [1830 40; < L discriminant (s. of… …   Universalium

• 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

• Quadratic field — In algebraic number theory, a quadratic field is an algebraic number field K of degree two over Q. It is easy to show that the map d ↦ Q(√d) is a bijection from the set of all square free integers d ≠ 0, 1 to the set of… …   Wikipedia

• Monogenic field — In mathematics, a monogenic field is an algebraic number field K for which there exists an element a such that the ring of integers OK is the polynomial ring Z[a]. The powers of such an element a constitute a power integral basis. In a monogenic… …   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

• Fundamental discriminant — In mathematics, a fundamental discriminant d is an integer that is the discriminant of a quadratic field. There is exactly one quadratic field with given discriminant, up to isomorphism.There are explicit congruence conditions that give the set… …   Wikipedia

• Conductor-discriminant formula — In mathematics, the conductor discriminant formula is a formula calculating the discriminant of a finite Galois extension L / K of global fields from the global Artin conductors of the irreducible characters Irr(G) of the Galois group G = G(L /… …   Wikipedia

• Conductor (class field theory) — In algebraic number theory, the conductor of a finite abelian extension of local or global fields provides a quantitative measure of the ramification in the extension. The definition of the conductor is related to the Artin map. Contents 1 Local… …   Wikipedia

• List of mathematics articles (D) — NOTOC D D distribution D module D D Agostino s K squared test D Alembert Euler condition D Alembert operator D Alembert s formula D Alembert s paradox D Alembert s principle Dagger category Dagger compact category Dagger symmetric monoidal… …   Wikipedia