有限域和伽罗华环讲义

作者简介

有限域和伽罗华环讲义（英文版），ISBN：9787506272919，作者：万哲先 著

书籍目录

1　Sets and Integers　1.1　Sets and Maps　1.2　The Factorization of Integers　1.3　Equivalence Relation and Partition　1.4　Exercises2　Groups　2.1　The Concept of a Group and Examples　2.2　Subgroups and Cosets　2.3　Cyclic Groups　2.4　Exercises3　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　Exercises4　Polynomials　4.1　Polynomial Rings　4.2　Division Algorithm　4.3　Euclidean Algorithm　4.4　Unique Factorization of Polynomials　4.5　Exercises5　Residue Class Rings　5.1　Residue Class Rings　5.2　Examples　5.3　Residue Class Fields　5.4　More Examples　5.5　Exercises6　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　Exercises7　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　Exercises8　Bases　8.1　Bases and Polynomial Bases　8.2　Dual Bases……9  Factoring Polynomails over Finite Fields10  Irreducible Polymials over Finite Fields11  Quadratic Forms over Finite Fields12  More Group Theory and Ring Theory13  Hensel's Lemma and Hensel Lift14  Galois RingsBibliographyIndex

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