Abstract Algebra

CLAUDIA MENINI  University of Ferrara , Ferrera, Italy . FREDDY VAN OYSTAEYEN  University of Antwerp, UIA, Antwerp, Belgium.

• Sets. Maps. Cartesian Product and Binary Relations. Posets, Lattices, Zorn's Lemma. Peano's Axions. Cardinality. Quotient Sets. Groupoids, Semigroups, Monoids. Groups. The Integers. Congruences. Normal Subgroups. Isomorphism Theorems for Groups. Cyclic Groups. Direct Product of Groups. The Symmetric Group. Further Results on Groups. Rings, Ideals, and Homomorphisms. Quotient Rings. Direct Product of Rings.

"This is a comprehensive book of over 750 pages, that covers the material of algebra courses in the first two or three years of a bachelor's degree program. …This a nice book is written in a very clear and explanatory style, offering a self-contained presentation and complete proofs, as well as well-chosen exercises, illustrative examples, and some interesting historical notes."-Mathematical Reviews, Issue 2005e"Many examples and worked exercises make the text easy to read. Written in a clear and detailed style it will be a valuable basis for students who want to learn algebra from the beginning."-H. Mitsch, Wien, Monatshefte für Mathematik"The experience of the authors together with a careful presentation of material makes this book a valuable addition to modern textbooks in algebra."-EMS Newsletter, June 2005