algebraic unit
11Dirichlet's unit theorem — In mathematics, Dirichlet s unit theorem is a basic result in algebraic number theory due to Gustav Lejeune Dirichlet.[1] It determines the rank of the group of units in the ring OK of algebraic integers of a number field K. The regulator is a… …
12Imaginary unit — i in the complex or cartesian plane; real numbers fall on the horizontal axis, and imaginary numbers fall on the vertical axis In mathematics, the imaginary unit allows the real number system ℝ to be extended to the complex number system ℂ, which …
13Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …
14Discriminant 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.… …
15S-unit — In mathematics, in the field of algebraic number theory, an S unit generalises the idea of unit of the ring of integers of the field. Many of the results which hold for units are also valid for S units.DefinitionLet K be a number field with ring… …
16Cyclotomic unit — In mathematics, a cyclotomic unit is a unit of an algebraic number field of the form (ζn − 1)/(ζ − 1) for ζ a root of unity, or more generally a unit that can be written as a product of these and a root of unity. The… …
17List of algebraic number theory topics — This is a list of algebraic number theory topics. Contents 1 Basic topics 2 Important problems 3 General aspects 4 Class field theory …
18Chain (algebraic topology) — This article is about algebraic topology. For the term chain in order theory, see chain (order theory). In algebraic topology, a simplicial k chain is a formal linear combination of k simplices.[1] Integration on chains Integration is defined on… …
19Polarization of an algebraic form — In mathematics, in particular in algebra, polarization is a technique for expressing a homogeneous polynomial in a simpler fashion by adjoining more variables. Specifically, given a homogeneous polynomial, polarization produces a multilinear form …
20Siemens (unit) — The siemens (symbol: S) is the SI derived unit of electric conductance and electric admittance. Conductance and admittance are the reciprocals of resistance and impedance respectively, hence one siemens is equal to the reciprocal of one ohm, and… …
