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# A course in algebra /

Fan, Yun.

A course in algebra / Yun Fan, Q.Y. Xiong, Y.L. Zheng. - Singapore ; River Edge, N.J. : World Scientific, ©2000. - 1 online resource (x, 246 pages) : illustrations

Includes index.

Preliminaries Sets Logic Relations Zorn's Lemma Groups Transformations and Permutations Groups Subgroups Homomorphisms, Isomorphisms Cosets Normal Subgroups, Quotient Groups Homomorphism Theorems Cyclic Groups, Orders of Elements Direct Products Rings Fundamentals Zero Divisors, Invertible Elements Ideals, Residue Rings Homomorphism Theorems Prime Ideals, Maximal Ideals Direct Sums Fraction Fields of Integral Domains Polynomial Rings Factorial Domains Polynomial Rings over Factorial Rings Modules Modules Homomorphisms Direct Products, Direct Sums Exact Sequences of Homomorphisms Free Modules, Matrices over Rings Matrices over Division Rings Matrices over Commutative Rings Algebras over Commutative Rings Tensor Products Projective Modules, Injective Modules Fields Subfields and Extensions Single Extensions Algebraic Extensions Splitting Fields, Normal Extensions Two Applications Separability, Multiple Roots Finite Fields Coding p-adic Numbers Quaternions 1 1 -- 1.1 1 -- 1.2 4 -- 1.3 7 -- 1.5 18 -- 2 19 -- 2.1 19 -- 2.2 27 -- 2.3 35 -- 2.4 39 -- 2.5 45 -- 2.6 49 -- 2.7 52 -- 2.8 56 -- 2.9 62 -- 3 71 -- 3.1 71 -- 3.2 77 -- 3.3 81 -- 3.4 86 -- 3.5 89 -- 3.6 93 -- 3.7 97 -- 3.8 101 -- 3.9 110 -- 3.10 117 -- 4 123 -- 4.1 123 -- 4.2 127 -- 4.3 133 -- 4.4 137 -- 4.5 142 -- 4.6 150 -- 4.7 159 -- 4.8 164 -- 4.9 171 -- 4.10 176 -- 5 183 -- 5.1 183 -- 5.2 187 -- 5.3 192 -- 5.4 196 -- 5.5 202 -- 5.6 207 -- 5.7 215 -- 5.8 220 -- 5.9 229 -- 5.10 238.

This volume is based on the lectures given by the authors at Wuhan University and Hubei University in courses on abstract algebra. It presents the fundamental concepts and basic properties of groups, rings, modules and fields, including the interplay between them and other mathematical branches and applied aspects.

9789812815095 9812815090

Algebra, Abstract.
MATHEMATICS--Algebra--Abstract.
Algebra, Abstract.
Algebra
Einführung
Algebra.
Álgebra.
Álgebra abstrata.

Electronic books.
Electronic books.

QA162 / .F36 2000eb

512/.02