Advanced Algebra Along with a companion volume Basic Algebra /

• Main Author: Knapp, Anthony W. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2008.
• Series: Cornerstones,
• Subjects: Mathematics.; Algebra.; Algebraic geometry.; Category theory (Mathematics).; Homological algebra.; Field theory (Physics).; Nonassociative rings.; Rings (Algebra).; Number theory.; Non-associative Rings and Algebras.; Field Theory and Polynomials.; Algebraic Geometry.; Number Theory.; Category Theory, Homological Algebra.

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. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and fea...

Table of Contents:

• 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.