Algebra: Groups, Rings, and Fields

Note: this book is a reprint edition.  See our review of the original A K Peters edition.

 

This text is an undergraduate abstract algebra textbook intended to be used for an upper level year-long sequence. The book, adapted from notes by the author, Louis Rowen, concisely introduces and motivates foundational abstract algebra concepts. 

 

Algebra is comprehensive in covering the standard topics of a two-semester undergraduate algebra sequence. Every one of the 27 chapters is followed by a collection of about 10 exercises of varying difficulties and themes. Unlike other popular abstract algebra textbooks, this text covers all of the group theory topics before moving on to rings then to fields.  

 

It is assumed that the reader is familiar at the outset with proof techniques and mathematical notation. The only applications that appear in the text are to other areas of mathematics, primarily number theory. Relative to the most popular undergraduate algebra texts, this one is shorter and has fewer examples.

 

I would recommend this book as a supplement for an advanced undergraduate abstract algebra course. It could be a good supplement to quality instruction and in-class time.

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Mckenzie West is an assistant professor at the University of Wisconsin - Eau Claire. Her mathematical research is in the field of computational number theory and arithmetic geometry.