Algebra : groups, rings and fields / Louis Rowen.

AUTOR: Louis Rowen
ISBN: 1568810288
IDIOMA: eng
PÁGINAS: XXII, 239
AÑO: 1994

 
   
RECOMENDADO EN LAS SIGUIENTES ASIGNATURAS
Estructuras algebraicas
Teoría de Galois
 
RESUMEN

This text presents the concepts of higher algebra in a comprehensive and modern way for self-study and as a basis for a high-level undergraduate course. The author is one of the preeminent researchers in this field and brings the reader up to the recent frontiers of research including never-before-published material
 
INDICE

Preface
Table of Principal Notation
Prerequisites
Pt. I Groups 1
Ch. 1 Monoids and Groups 2
Ch. 2 How to Divide: Lagrange's Theorem, Cosets, and an Application to Number Theory 8
Ch. 3 Cauchy's Theorem: How to Show a Number Is Greater Than 1 15
Ch. 4 Introduction to the Classification of Groups: Homomorphisms, Isomorphisms, and Invariants 23
Ch. 5 Normal Subgroups - The Building Blocks of the Structure Theory 29
Ch. 6 Classifying Groups - Cyclic Groups and Direct Products 39
Ch. 7 Finite Abelian Groups 46
Ch. 8 Generators and Relations 56
Ch. 9 When Is a Group a Group? (Cayley's Theorem) 66
Ch. 10 Recounting: Conjugacy Classes and the Class Formula 72
Ch. 11 Sylow Subgroups: A New Invariant 79
Ch. 12 Solvable Groups: What Could Be Simpler? 86
Pt. II Rings and Polynomials 97
Ch. 13 An Introduction to Rings 98
Ch. 14 The Structure Theory of Rings 103
Ch. 15 The Field of Fractions - A Study in Generalization 109
Ch. 16 Polynomials and Euclidean Domains 114
Ch. 17 Principal Ideal Domains: Induction without Numbers 124
Ch. 18 Roots of Polynomials 133
Ch. 19 (Optional) Applications: Famous Results from Number Theory 138
Ch. 20 Irreducible Polynomials 146
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