Free Download From Rings and Modules to Hopf Algebras: One Flew over the Algebraist's Nest
English | 2024 | ISBN: 303150061X | 528 Pages | PDF (True) | 9 MB
Throughout the book, the exposition relies on universal constructions, making systematic use of quotients and category theory ― whose language is introduced in the first chapter. The book is divided into four parts. Parts I and II cover foundations of rings and modules, field theory and generalities on finite group representations, insisting on rings of polynomials and their ideals. Part III culminates in the structure theory of finitely generated modules over Dedekind domains and its applications to abelian groups, linear maps, and foundations of algebraic number theory. Part IV is an extensive study of linear representations of finite groups over fields of characteristic zero, including graded representations and graded characters as well as a final chapter on the Drinfeld-Lusztig double of a group algebra, appearing for the first time in a textbook at this level.