有限场及伽罗瓦环讲义LECTURES ON FINITE FIELDS AND GALOIS RINGS
点此进入淘宝搜索页搜索分類: 图书,进口原版书,科学与技术 Science & Techology ,
作者： Zhe-Xian Wan 著
出 版 社： Penguin
出版时间： 2003-12-1字数：版次： 1页数： 342印刷时间： 2003/08/01开本：印次： 1纸张： 胶版纸I S B N ： 9789812385048包装： 精装内容简介
This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.
目录
1 Sets and Integers
1.1 Sets and Maps
1.2 The Factorization of Integers
1.3 Equivalence Relation and Partition
1.4 Exercises
2 Groups
2.1 The Concept of a Group and Examples
2.2 Subgroups and Cosets
2.3 Cyclic Groups
2.4 Exercises
3 Fields and Rings
3.1 Fields
3.2 The Characteristic of a Field
3.3 Rings and Integral Domains
3.4 Field of Fractions of an Integral Domain
3.5 Divisibility in a Ring
3.6 Exercises
4 Polynomials
4.1 Polynomial Rings
4.2 Division Algorithm
4.3 Euclidean Algorithm
4.4 Unique Factorization of Polynomials
4.5 Exercises
5 Residue Class Rings
5.1 Residue Class Rings
5.2 Examples
5.3 Residue Class Fields
5.4 More Examples
5.5 Exercises
6 Structure of Finite Fields
6.1 The Multiplicative Group of a Finite Field
6.2 The Number of Elements in a Finite Field
6.3 Existence of Finite Field with pn Elements.
6.4 Uniqueness of Finite Field with pn Elements
6.5 Subfields of Finite Fields
6.6 A Distinction between Finite Fields of Characteristic 2 and Not 2
6.7 Exercises
7 Further Properties of Finite Fields
7.1 Automorphisms
7.2 Characteristic Polynomials and Minimal Polynomials .
7.3 Primitive Polynomials
7.4 Trace and Norm
7.5 Quadratic Equations
7.6 Exercises
8 Bases
8.1 Bases and Polynomial Bases
8.2 Dual Bases
……
9 Factoring Polynomials over finite fields
10 Irreducible Polynomials over Finite Fields
11 Quadratic Formas Over Finite Fields
12 More Group Theory and Ring Theory
13 Hensel's Lemma and Hensel Lift
14 Galois Rings
Bibliography
Index
