ramification degree
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Ramification (botany) — Ramification, in botany, is the divergence of the stem and limbs of a plant into smaller ones, i.e. trunk into branches, branches into increasingly smaller branches, etc. Gardeners stimulate the process of ramification through pruning, thereby… … Wikipedia
Ramification theory of valuations — In mathematics, the ramification theory of valuations studies the set of extensions of a valuation v of a field K to an extension L of K. It is a generalization of the ramification theory of Dedekind domains. Contents 1 Galois case 1.1… … 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
Splitting of prime ideals in Galois extensions — In mathematics, the interplay between the Galois group G of a Galois extension L of a number field K, and the way the prime ideals P of the ring of integers OK factorise as products of prime ideals of OL, provides one of the richest parts of… … Wikipedia
Valuation (algebra) — In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field. They generalize to commutative algebra the notion of size… … 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 — 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
Riemann-Hurwitz formula — In mathematics, the Riemann Hurwitz formula, named after Bernhard Riemann and Adolf Hurwitz, describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other. It therefore connects ramification… … Wikipedia
Hyperelliptic curve — In algebraic geometry, a hyperelliptic curve (over the complex numbers) is an algebraic curve given by an equation of the form:y^2 = f(x)where f(x) is a polynomial of degree n > 4 with n distinct roots. A hyperelliptic function is a function from … Wikipedia
Charles Sanders Peirce — B … Wikipedia
Bonsai aesthetics — on display at at the Chinese Penjing Collection of National Bonsai Penjing Museum, Washington. The tree displays several aesthetic qualities common to bonsai including miniaturization, leaf reduction, lignification, ramification and curvature. As … Wikipedia
