Algebra: Chapter 0 (second printing with corrections)

This is the 2nd printing (many typos corrected) P.S. (Dec 2023) Even though many errors have been corrected in this second (2016) reprint, a rather large number of errors (some quite notable) remain -- for the errata on this printing, visit: [url]https://www.math.fsu.edu/~aluffi/algebraerrata.2016/Errata.html[/url] Algebra: Chapter 0 Is A Self-contained Introduction To The Main Topics Of Algebra, Suitable For A First Sequence On The Subject At The Beginning Graduate Or Upper Undergraduate Level. The Primary Distinguishing Feature Of The Book, Compared To Standard Textbooks In Algebra, Is The Early Introduction Of Categories, Used As A Unifying Theme In The Presentation Of The Main Topics. A Second Feature Consists Of An Emphasis On Homological Algebra: Basic Notions On Complexes Are Presented As Soon As Modules Have Been Introduced, And An Extensive Last Chapter On Homological Algebra Can Form The Basis For A Follow-up Introductory Course On The Subject. Approximately 1,000 Exercises Both Provide Adequate Practice To Consolidate The Understanding Of The Main Body Of The Text And Offer The Opportunity To Explore Many Other Topics, Including Applications To Number Theory And Algebraic Geometry. This Will Allow Instructors To Adapt The Textbook To Their Specific Choice Of Topics And Provide The Independent Reader With A Richer Exposure To Algebra. Many Exercises Include Substantial Hints, And Navigation Of The Topics Is Facilitated By An Extensive Index And By Hundreds Of Cross-references.--jacket. Preliminaries: Set Theory And Categories -- Groups, First Encounter -- Rings And Modules -- Groups, Second Encounter -- Irreducibility And Factorization In Integral Domains -- Linear Algebra -- Fields -- Linear Algebra, Reprise -- Homological Algebra. Paolo Aluffi. Includes Index. Cover 1 Title page 4 Contents 6 Introduction 18 Chapter I. Preliminaries: Set theory and categories 24 Chapter II. Groups, first encounter 64 Chapter III. Rings and modules 142 Chapter IV. Groups, second encounter 210 Chapter V. Irreducibility and factorization in integral domains 266 Chapter VI. Linear algebra 328 Chapter VII. Fields 408 Chapter VIII. Linear algebra, reprise 506 Chapter IX. Homological algebra 582 Index 722 Back Cover 738