$\newcommand{\aatavdots}[1]{\vdots} \newcommand{\codeword}{} \newcommand{\identity}{\mathrm{id}} \newcommand{\notdivide}{\nmid} \newcommand{\notsubset}{\not\subset} \newcommand{\lcm}{\operatorname{lcm}} \newcommand{\gf}{\operatorname{GF}} \newcommand{\inn}{\operatorname{Inn}} \newcommand{\aut}{\operatorname{Aut}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\cis}{\operatorname{cis}} \newcommand{\chr}{\operatorname{char}} \newcommand{\Null}{\operatorname{Null}} \newcommand{\transpose}{\text{t}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \definecolor{fillinmathshade}{gray}{0.9} \newcommand{\fillinmath}[1]{\mathchoice{\colorbox{fillinmathshade}{$\displaystyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\textstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptstyle \phantom{\,#1\,}$}}{\colorbox{fillinmathshade}{$\scriptscriptstyle\phantom{\,#1\,}$}}} $

Dedication About This Edition

This edition was adapted from Thomas W. Judson’s open-source Abstract Algebra: Theory and Applications for use in MATH 4043 by Nicholas Touikan, working together with Claude, Anthropic’s AI model, which carried out most of the restructuring, drafting, and editing under his direction; Nicholas Touikan also revised several proofs by hand where the reordering of chapters required it. Several chapters were removed, two new chapters (Groups and The Simplicity of $A_n$) were written to carry forward just the results this edition still depends on, the remaining chapters were reordered, and all Sage-related material was removed. A full summary of the changes appears in the Colophon at the end of this text. The original, unabridged text and its PreTeXt source are freely available at github.com/twjudson/aata.

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