Introduction to Abstract Algebra

Undergraduates will appreciate the accessibility of this treatment of groups, rings and fields, largely because Nicholson (mathematics and statistics, U. of Calgary) helps them advance to abstract theory by means of concrete examples of induction, number theory, integers modulo n and permutations before defining abstract structures. This edition, which includes new sections on modules(free, semisimple and projective), modules over principal ideal domains, semidirect products, and the Wedderburn-Artin theorem also includes new appendices on Zorn's lemma and the proof of the recursive theorem. Nicholson starts with a review of proofs, sets, mappings and equivalences, then in 11 chapters covers integers and permutations, groups, rings, polynomials, factorization in integral domains, fields, modules over principal ideal domains, p-groups and the Sylow theorems, series of subgroups, Galois theory and finiteness conditions for rings and modules. He includes appendices on complex numbers and matric arithmetic and offers selected answers for exercises. Annotation c2007 Book News, Inc., Portland, OR (booknews.com)

W. KEITH NICHOLSON, PhD, is a Professor in the Department of Mathematics and Statistics at the University of Calgary in Alberta, Canada. Dr. Nicholson has published numerous textbooks and monographs throughout his career. He received his PhD in Pure Mathematics from the University of California at Santa Barbara, and his current research interests include clean rings, morphic rings, and module theory.