File:NLC416-08jh013673-31468 代數整數論.pdf

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代數整數論   (Wikidata search (Cirrus search) Wikidata query (SPARQL)  Create new Wikidata item based on this file)
Author
蕭君絳譯纂
image of artwork listed in title parameter on this page
Title
代數整數論
Publisher
國立武漢大學數學室[發行者]
Description

目錄
第一篇 一般論
第一章 代數整數
1.1 代數數
1.2 代數體
1.23 g －數
1.3 代數整數
1.4 整除
1.5 單位
第二章 代數體之整數「伊德耶」
2.1 代數體中整數之底
2.2 「伊德耶」
2.3 「伊德耶」之積
2.4 「伊德耶」之整除
2.41 最小公倍數
2.42 最大公約數
2.5 「伊德耶」論之基本定理
2.6 整係數之多項式「伊德耶」因子
第三章 剩餘類
3.1 合同式
3.2 剩餘類
3.3 範數
3.4 素p之範數
3.5 剩餘類之四則
3.51 一次合同式
3.6 h（p）之理論
3.61 h（p）中多項式
3.7 代數體中之euler函數cp（m）
3.8 關於素p之冪者之剩餘環h（pm）
第四章 「伊德耶」之類別，形勢空間
4.1 分數「伊德耶」
4.2 「伊德耶」群。「伊德耶」類
4.3 形勢空間之定義
4.4 近傍
4.5 同型
4.6 通集合及可數公理
4.7 封集合
4.8 形勢積
第五第 minkowaki氏定理之應用.形勢群
5.1 minkowski氏定理
5.2 關於代數體之判別式理論
5.3 形勢群之定義
5.4 單位之近傍系
5.5 部分群.因子群
5.6 同型態.准同型態
5.7 通群.全離群
第六章 相對體
6.1 代數體之擴張
6.2 「伊德耶」之延長
6.3 共軛「伊德耶」相對範數
6.4 k/k中之β
6.5 「伊德耶」之值
6.51 「伊德耶」之形勢群
第七章 判別式.共軛差積
7.1 數之共軛差積與判別式
7.2 代數體之共軛差積
7.3 dedekiud氏方法
7.4 總括
7.5 k/k中p之分解之形式的表現
7.6 dedekind氏判別定理
第八章 galois體
8.1 galois體之置換群
8.2 分解體
8.3 惰性體
8.4 任意體ω/k中之素因子分解
8.5 共軛差積εk/k,εω/k
8.6 分歧體
8.7 中間體之分歧
8.8 判別定理（εk/k之β成分）
8.9 圓體
8.10 圓體中之素因子分解
8.11 kronecker氏定理
8.12 無限體上galoib體中之素因子分解
8.13 無限體上之任意有限擴張
第九章 單位
9.1 虛二次體之單位
9.2 1之根
9.3 diriclilet氏單位定理
9.31 單位規定數
9.4 gnlois體之單位
9.5 相對galois體之單位
第二篇 類體論
第十章 合同類別.無限體之galois群
10.1 數之乘群（乘法合同）
10.2 數之乘群（符號分布）
10.3 狹義之「伊德耶」類（合同類）
10.4 「伊德耶」群之先導
10.5 galois群與形勢群
10.6 非閉部分群之存在
10.7 可數galois體
第十一章 解析上之考察
11.1 類中「伊德耶」之密度
11.2 代數體之ζ函數
11.3 l函數
11.4 關於galois體之考察
11.5 類體之定義
11.6 算術級數之定理
11.7 類體雛型之分圓體
11.8 無限abel群之指標
第十二章 基本定理
12.1 abel體之基本定理
12.2 特異類之數a
12.3 問題之變形
12.4 （1）之證
12.5 范剩餘之群指數、（ⅱ）之證
12.6 p進法
12.61 p進體中之exux,logx
12.7 （ⅱ）證完結
12.8 類體之結合定理
12.9 類體之一意性
第十三章 分解定理.同態定理.互反律
13.1 基本定理補強
13.2 artin氏互反律
13.3 類體之推進定理
13.4 一般分圓體
13.5 frobenius置換之性質
13.6 記號定義之擴張
13.7 目標單純化
13.8 一般分圓體中之互反律
13.9 artin氏補助定理
13.10 互反律之證明（巡迴體）
13.11 互反律之證明（完結）
第十四章 存在定理 先導定理
14.1 kummer體
14.2 kummer體中之素因子分解
14.3 kummer體之先導
14.4 存在證明之補助定理
14.5 存在證明（kummer）
14.52 冪剩餘之群指數
14.58 證明之完結
14.6 存在證明（一般者）
14.7 abel體之先導
第十五章 終結定理
15.1 密度
15.2 tsehebotareff之密度定理
15.3 終結定理
第十六章 二次體論
16.1 二次體之先導
16.2 互反律
16.3 二次體之特異類
16.4 二次體之種
第十七章 分圓體之類數
17.1 furtwangler之定理
17.2 分圓體之單位
17.3 分圓體之類數計算
17.4 ganss和
17.5 任意分圓體之類數
17.6 二次體之類數
第三篇 單項化問題
第十八章 單項化問題
18.1 hilbert之豫想
18.2 問題之群論化
18.3 亞abel群之構造與因子團
18.4 分裂群
18.5 h之元數「伊德耶」
18.6 單項化定理之證明
第四篇 局限類體論
第十九章 多元數論上之準備
19.1 巡迴多元環
19.2 關於單純環之二定理
第二十章 p進數體上之多元體
20.1 p進數體上之多元體之整數論
20.2 （可換）擴張體
20.3 〓進多元體之構造
第二十一章 局限類體論.范剩餘記號
21.1 巡迴擴張體
21.2 abel擴張體
21.3 存在定理之證明
21.4 一般推進定理
21.5 hilbert之記號

Language Chinese
Publication date 民國33[1944]
Source
institution QS:P195,Q732353
(民國時期文獻 民國圖書)
主題
InfoField
代數整數
中圖分類
InfoField
O156.1
載體形態
InfoField
298頁

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