Advanced Algebra, 2008 Cornerstones Series

Langue : Anglais

Auteur : Knapp Anthony W.

Couverture de l’ouvrage Advanced Algebra

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Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Together the two books give the reader a global view of algebra, its role in mathematics as a whole and are suitable as texts in a two-semester advanced undergraduate or first-year graduate sequence in algebra.

Transition to Modern Number Theory.- Wedderburn–Artin Ring Theory.- Brauer Group.- Homological Algebra.- Three Theorems in Algebraic Number Theory.- Reinterpretation with Adeles and Ideles.- Infinite Field Extensions.- Background for Algebraic Geometry.- The Number Theory of Algebraic Curves.- Methods of Algebraic Geometry.

Focuses on algebraic number theory and algebraic geometry, and the distinctions and influences of each topic on the other Presents material vital to the knowledge of the professional mathematician Comprehensive text ideal for the classroom or self-study