| 書目名稱 | From Rings and Modules to Hopf Algebras | | 副標(biāo)題 | One Flew Over the Al | | 編輯 | Michel Broué | | 視頻video | http://file.papertrans.cn/349/348914/348914.mp4 | | 概述 | A highly original introduction to basic tools of algebra, from a categorical point of view.Includes advanced material on representation theory such as the Drinfeld–Lusztig double.Unusually rich in exa | | 圖書封面 |  | | 描述 | This textbook provides an introduction to fundamental concepts of algebra at upper undergraduate to graduate level, covering the theory of rings, fields and modules, as well as the representation theory of finite groups..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..Based on over twenty years of teaching various aspects of algebra, mainly at the école Normale Supér | | 出版日期 | Textbook 2024 | | 關(guān)鍵詞 | Polynomial rings; Ideals; Principal ideal domain; Dedekind ring; Modules; Discriminant; Resultant; Represen | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-50062-6 | | isbn_ebook | 978-3-031-50062-6 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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