Abstract Algebra: A Comprehensive Treatise - From First Principles to the Research Frontier

Abstract algebra is the mathematics of structure: the language in which symmetry becomes a group, arithmetic a ring, linearity a module, and solvability a question about field extensions. This comprehensive treatise develops the subject from first principles to the research frontier, covering groups, rings, modules, fields, Galois theory, commutative algebra, homological algebra, representation theory, and category theory with full proofs and computational examples throughout.