Euclidean domain：歐幾里得整環
歐幾里得整環
在抽象代數中，歐幾里得整環（Euclideandomain）是一種能作輾轉相除法的整環。凡...文獻編輯.Motzkin.TheEuclideanalgorithm,Bull.Amer.Math.Soc.55,(1949) ...。其他文章還包含有：「2.2EuclideanDomains」、「20.EuclideanDomainsLetRbeanintegral...」、「8.3」、「AbstractAlgebra」、「Euclideandomain」、「EuclideandomaininnLab」、「ringtheory」、「代數導論二Week2(Part3)」
查看更多 離開網站維基百科，自由的百科全書在抽象代數中，歐幾里得整環（Euclideandomain）是一種能作輾轉相除法的整環。凡歐幾里得整環必為主理想環。一個歐幾里得整環是一整環D{\displaystyleD}及函數v:D∖{0}→N∪{0}{\displaystylev:D\setminus\{0\}\to\mathbb{N}\cup\{0\}}，使之滿足下述性質：函數v{\displaystylev}可設想成元素大小的量度，當D=Z{\displaystyleD=\mathbb{Z}}時可取v(x):=|x|{\displaystylev(x):=|x|}。歐幾理得整環的例子包括了：利用輾轉相除法（定義中的第一條性質），可以證明歐幾里得環必為主理想環，此時理想由其中v{\displa...
2.2 Euclidean Domains
https://www.math.utah.edu
20. Euclidean Domains Let R be an integral ...
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The ring Z is a Euclidean domain. The function d is the absolute value. Definition 20.3. Let R be a ring and let f ∈ R[x] be a ...
8.3
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The norm on polynomials is the degree of the polynomial. Definition 8.2.1: Euclidean Domain. A Euclidean domain is an integral domain R ...
Abstract Algebra
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Euclidean domain
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In mathematics, more specifically in ring theory, a Euclidean domain is an integral domain that can be endowed with a Euclidean function which allows a ...
Euclidean domain in nLab
https://ncatlab.org
A Euclidean domain is an integral domain which admits a form of the Euclidean quotient-and-remainder algorithm familiar from school ...
ring theory
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An integral domain E is called Euclidean domain if there exist a function (often called as norm) f from non zero elements of E to the non ...
代數導論二Week 2 (Part 3)
https://hackmd.io
Euclidean Domain 就是一個integral domain 上面加一個norm，也就是一個把環打到正整數或0 0 的函數，唯一的要求就是把0 0 打到0 0 。 例子：整數. 舉例來說Z Z 搭配取 ...