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A First Course in Abstract Algebra

A First Course in Abstract Algebra

Author(s):
  • John B. Fraleigh
  • Neal Brand
    • Author: John B. Fraleigh
    • ISBN:9789356067059
    • 10 Digit ISBN:9356067058
    • Price:Rs. 1025.00
    • Pages:444
    • Imprint:Pearson Education
    • Binding:Paperback
    • Status:Available


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    A First Course in Abstract Algebra, 8th Edition retains its hallmark goal of covering all the topics needed for an in-depth introduction to abstract algebra — and is designed to be relevant to future graduate students, future high school teachers, and students who intend to work in industry. New co-author Neal Brand has revised this classic text carefully and thoughtfully, drawing on years of experience teaching the course with this text to produce a meaningful and worthwhile update. This in-depth introduction gives students a firm foundation for more specialized work in algebra by including extensive explanations of the what, the how, and the why behind each method the authors choose.

    Table of Content

    "I. GROUPS AND SUBGROUPS Binary Operations Groups Abelian Groups Nonabelian Examples Subgroups Cyclic Groups Generating Sets and Cayley Digraphs II. STRUCTURE OF GROUPS Groups and Permutations Finitely Generated Abelian Groups Cosets and the Theorem of Lagrange Plane Isometries III. HOMOMORPHISMS AND FACTOR GROUPS Factor Groups Factor-Group Computations and Simple Groups Groups Actions on a Set Applications of G -Sets to Counting IV. ADVANCED GROUP THEORY Isomorphism Theorems Sylow Theorems Series of Groups Free Abelian Groups Free Groups Group Presentations V. RINGS AND FIELDS Rings and Fields Integral Domains Fermat's and Euler's Theorems Encryption VI. CONSTRUCTING RINGS AND FIELDS The Field of Quotients of an Integral Domain Rings and Polynomials Factorization of Polynomials over Fields Algebraic Coding Theory Homomorphisms and Factor Rings Prime and Maximal Ideals Noncommutative Examples VII. COMMUTATIVE ALGEBRA Vector Spaces Unique Factorization Domains Euclidean Domains Number Theory Algebraic Geometry Gröbner Basis for Ideals VIII. EXTENSION FIELDS Introduction to Extension Fields Algebraic Extensions Geometric Constructions Finite Fields IX. Galois Theory Introduction to Galois Theory Splitting Fields Separable Extensions Galois Theory Illustrations of Galois Theory Cyclotomic Extensions Insolvability of the Quintic"

    Salient Features

    "• A focus on groups, rings and fields gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures. • Gives clear and concise explanations of the theory, with well-thought-out examples to highlight key points and clarify more difficult concepts. • UPDATED - Many exercises in the text have been updated, and many are new. Most exercise sets are broken down into parts consisting of computations, concepts, and theory. • NEW - Applied topics — such as RSA encryption and coding theory as well as examples of applying Gröbner bases — have been added to the 8th Edition. • Historical notes written by Victor Katz, an authority on the history of math, provide valuable perspective."