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Zusatztext "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 Informationen zum Autor CLAUDIA MENINI University of Ferrara , Ferrera, Italy . FREDDY VAN OYSTAEYEN University of Antwerp, UIA, Antwerp, Belgium. Klappentext In one exceptional volume! Abstract Algebra covers subject matter typically taught over the course of two or three years and offers a self-contained presentation! detailed definitions! and excellent chapter-matched exercises to smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe! this ambitious! comprehensive book includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory and explains sets! maps! posets! lattices! and other essentials of the algebraic language; Peano's axioms and cardinality; groupoids! semigroups! monoids! groups; and normal subgroups. Zusammenfassung In one exceptional volume, Abstract Algebra covers subject matter typically taught over the course of two or three years and offers a self-contained presentation, detailed definitions, and excellent chapter-matched exercises to smooth the trajectory of learning algebra from zero to one. Field-tested through advance use in the ERASMUS educational project in Europe, this ambitious, comprehensive book includes an original treatment of representation of finite groups that avoids the use of semisimple ring theory and explains sets, maps, posets, lattices, and other essentials of the algebraic language; Peano's axioms and cardinality; groupoids, semigroups, monoids, groups; and normal subgroups. Inhaltsverzeichnis 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. ...
