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9780817671334

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From the reviews: <p> All together, this is another outstanding textbook written by the renowned and versatile mathematical researcher, teacher, and author Anthony W. Knapp that reflects his spirit, his devotion to mathematics, and his rich experiences in expository writing at best...This textbook is the second volume of Anthony W. Knapp's comprehensive introduction to the fundamental concepts and tools in modern abstract algebra. Together with its foregoing companion volume Basic Algebra, which was published in the autumn of 2006, the current book is to provide a global view of the subject, thereby particularly emphasizing both its various applications and its ubiquitous role in contemporary mathematics. As the author already pointed out in the preface to the first volume, his leading idea was to give a systematic account of what a budding mathematician needs to know about the principles of modern algebra in order to communicate well with colleagues in all branches of mathematics and related sciences. This rewarding program was masterly begun in the companion volume Basic Algebra, where the fundamentals of linear algebra, multilinear algebra, group theory, commutative algebra, field theory, Galois theory, and module theory over noncommutative rings were profoundly developed. a Zentralblatt Math <p> Advanced Algebra is a wonderfully useful and well-written book, characterized by clear and a ~user-friendlya (TM) treatments of many important algebraic topics. a ] Finally, Advanced Algebra contains a thorough coverage of GrAbner bases a ] and continues the trend set in Basic Algebra of providing good, meaningful (and plentiful) exercises. I highly recommend this wonderful book. (Michael Berg, MAA Online, January, 2008)

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