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This abstract algebra textbook takes an integrated approach that highlights the similarities of fundamental algebraic structures among a number of topics. The book begins by introducing groups, rings, vector spaces, and fields, emphasizing examples, definitions, homomorphisms, and proofs. The goal is to explain how all of the constructions fit into an axiomatic framework and to emphasize the importance of studying those maps that preserve the underlying algebraic structure. This fast-paced introduction is followed by chapters in which each of the four main topics is revisited and deeper results are proven. The second half of the book contains material of a more advanced nature. It includes a thorough development of Galois theory, a chapter on modules, and short surveys of additional algebraic topics designed to whet the reader's appetite for further study. This book is intended for a first introduction to abstract algebra and requires only a course in linear algebra as a prerequisite. The more advanced material could be used in an introductory graduate-level course.
I like that when a proof is started it is indicated by a bold "Proof." Then it proceeds with the proof in a well written written manner. Also, if it is a multi-part proof it indicates which part is currently being proved.I used Modern Algebra by Durbin in undergrad, and we are using Dummit & Foote in my grad course. I really enjoy having this book as a supplemental to the Dummit & Foote textbook because I personally feel that the explanations are better. I would have definitely preferred this textbook in my undergraduate abstract algebra course.
