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Algebra, 2 ed
◆Taylor & Francis セール開催中！：2025年9月28日(日)ご注文分まで
※上記表示の販売価格は割引適用後の価格です 未刊 ご予約承ります。 Groups, Rings, and Fields Series: Textbooks in Mathematics Author: Rowen, Louis Halle (Bar-Ilan University, Israel) / Vishne, Uzi Publisher: Taylor & Francis ISBN: 9780367231767 Cover: HARDCOVER Date: 2025年02月 こちらの商品は学校・法人様向け（機関契約）のオンラインブック版がございます。 オンラインブックの価格、納期につきましては弊社営業員または当ECサイトよりお問い合わせください。  DESCRIPTION Algebra is a subject we have become acquainted with during most of our mathematical education, often in connection with the solution of equations. Algebra: Groups, Rings, and Fields, Second Edition deals with developments related to their solutions. The principle at the heart of abstract algebra, a subject that enables one to deduce sweeping conclusions from elementary premises, is that the process of abstraction enables us to solve a variety of such problems with economy of effort. This leads to the glorious world of mathematical discovery. This second edition follows the original three-pronged approach: the theory of finite groups, number theory, and Galois’ amazing theory of field extensions tying solvability of equations to group theory. As algebra has branched out in many directions, the authors strive to keep the text manageable while at the same time introducing the student to exciting new paths. In order to support this approach, the authors broadened the first edition, giving monoids a greater role, and relying more on matrices. Hundreds of new exercises were added. A course in abstract algebra, properly presented, could treat mathematics as an art as well as a science. In this exposition, we try to present underlying ideas, as well as the results they yield. TABLE OF CONTENTS 1 Monoids and Groups 2 Lagrange’s Theorem, Cosets, and an Application to Number Theory 3 Cauchy’s Theorem: Showing that a Number Is Greater Than 1 4 Structure of Groups: Homomorphisms, Isomorphisms, and Invariants 5 Normal Subgroups: The Building Blocks of the Structure Theory 6 Classifying Groups: Cyclic Groups and Direct Products 7 Finite Abelian Groups 8 Generators and Relations 9 When Is a Group a Group? (Cayley’s Theorem) 10 Conjugacy Classes and the Class Equation 11 Sylow Subgroups 12 Solvable Groups: What Could Be Simpler? 13 Groups of Matrices 14 An Introduction to Rings 15 The Structure Theory of Rings 16 The Field of Fractions: A Study in Generalization 17 Polynomials and Euclidean Domains 18 Principal Ideal Domains: Induction without Numbers 19 Roots of Polynomials 20 Applications: Famous Results from Number Theory 21 Irreducible Polynomials 22 Field Extensions: Creating Roots of Polynomials 23 The Geometric Problems of Antiquity 24 Adjoining Roots to Polynomials: Splitting Fields 25 Finite Fields 26 The Galois Correspondence 27 Applications of the Galois Correspondence 28 Solving Equations by Radicals 29 Integral Extensions 30 Group Representations and their Characters 31 Transcendental Numbers: e and π 32 Skew Field Theory 33 Where Do We Go From Here?
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