# Algebraic number fields One may generalize this to " closed-form numbers ", which may be defined in various ways.

## Mathematical Treasure: Hilbert on Algebraic Number Fields

Most broadly, all numbers that can be defined explicitly or implicitly in terms of polynomials, exponentials, and logarithms are called "elementary numbers", and these include the algebraic numbers, plus some transcendental numbers. An algebraic integer is an algebraic number that is a root of a polynomial with integer coefficients with leading coefficient 1 a monic polynomial.

A crash course in Algebraic Number Theory

In this sense, algebraic integers are to algebraic numbers what integers are to rational numbers. The sum, difference and product of algebraic integers are again algebraic integers, which means that the algebraic integers form a ring.

The name algebraic integer comes from the fact that the only rational numbers that are algebraic integers are the integers, and because the algebraic integers in any number field are in many ways analogous to the integers. If K is a number field, its ring of integers is the subring of algebraic integers in K , and is frequently denoted as O K. These are the prototypical examples of Dedekind domains. From Wikipedia, the free encyclopedia.

## Equilateral triangulations of Riemann surfaces, and curves over algebraic number fields

Complex number that is a root of a non-zero polynomial in one variable with rational coefficients. Not to be confused with Algebraic solution. Main article: Closed-form number. Main article: Algebraic integer.

Algebraic numbers. Number systems. Cardinal numbers Irrational numbers Fuzzy numbers Hyperreal numbers Levi-Civita field Surreal numbers Transcendental numbers Ordinal numbers p -adic numbers Supernatural numbers Superreal numbers. Classification List.

## Lattice Index Codes From Algebraic Number Fields - IEEE Journals & Magazine

Categories : Algebraic numbers. Thanks in advance for your time. Skip to content. Search for books, journals or webpages All Pages Books Journals. View on ScienceDirect. Series Editors: Gerald Janusz.

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