Advanced Algebra

Livro digital

Título:
Advanced Algebra

Autor:
Anthony W. Knapp

Categoria:
Tecnologia > Geral

Doador:
Raffaello D. N.

Sinopse:
Advanced Algebra is structured for readers who already know the foundations and now need to see how modern algebra opens outward into number theory, ring theory, homological algebra, algebraic geometry, and related fields. Its table of contents makes that ambition explicit from the start, moving from quadratic reciprocity and Dirichlet's theorem into Wedderburn-Artin theory, the Brauer group, and derived functors before widening further into algebraic number theory and geometry. The material is not a narrow specialist text. Along the way it develops p-adic numbers, valuations, adeles and ideles, infinite field extensions, Grobner bases, divisors, the Riemann-Roch theorem, and the methods of affine and projective algebraic geometry. That breadth gives the book a clear identity as a serious second step after basic algebra, aimed at readers who want structure, proof, and long-range mathematical connections rather than isolated techniques. Anthony W. Knapp writes the book as both a reference and a course text, with problems, historical framing, and a guide for the reader reinforcing its teaching role. The result is a demanding but coherent map of advanced algebra, especially valuable for students who want to understand how classical algebraic topics connect to modern number theory, field theory, and geometry.