{"product_id":"a-first-course-in-abstract-algebra-9780201763904","title":"A First Course in Abstract Algebra","description":"\u003cp\u003e • Author(s): John Fraleigh\u003cbr\u003e • Publisher: Pearson\u003cbr\u003e • Publisher Imprint: Pearson\u003cbr\u003e • BISAC: Algebra - General\u003c\/p\u003e\u003cp\u003e\u003cb\u003e\u003c\/b\u003e Considered a classic by many, \u003cb\u003eA First Course in Abstract Algebra, Seventh Edition\u003c\/b\u003e is an in-depth introduction to abstract algebra. Focused on groups, rings and fields, this text gives students a firm foundation for more specialized work by emphasizing an understanding of the nature of algebraic structures.\u003c\/p\u003e  \u003cb\u003eKEY TOPICS: \u003c\/b\u003e Sets and Relations; GROUPS AND SUBGROUPS; Introduction and Examples; Binary Operations; Isomorphic Binary Structures; Groups; Subgroups; Cyclic Groups; Generators and Cayley Digraphs; PERMUTATIONS, COSETS, AND DIRECT PRODUCTS; Groups of Permutations; Orbits, Cycles, and the Alternating Groups; Cosets and the Theorem of Lagrange; Direct Products and Finitely Generated Abelian Groups; Plane Isometries; HOMOMORPHISMS AND FACTOR GROUPS; Homomorphisms; Factor Groups; Factor-Group Computations and Simple Groups; Group Action on a Set; Applications of G-Sets to Counting; RINGS AND FIELDS; Rings and Fields; Integral Domains; Fermat's and Euler's Theorems; The Field of Quotients of an Integral Domain; Rings of Polynomials; Factorization of Polynomials over a Field; Noncommutative Examples; Ordered Rings and Fields; IDEALS AND FACTOR RINGS; Homomorphisms and Factor Rings; Prime and Maximal Ideas; Gröbner Bases for Ideals; EXTENSION FIELDS; Introduction to Extension Fields; Vector Spaces; Algebraic Extensions; Geometric Constructions; Finite Fields; ADVANCED GROUP THEORY; Isomorphism Theorems; Series of Groups; Sylow Theorems; Applications of the Sylow Theory; Free Abelian Groups; Free Groups; Group Presentations; GROUPS IN TOPOLOGY; Simplicial Complexes and Homology Groups; Computations of Homology Groups; More Homology Computations and Applications; Homological Algebra; Factorization; Unique Factorization Domains; Euclidean Domains; Gaussian Integers and Multiplicative Norms; AUTOMORPHISMS AND GALOIS THEORY; Automorphisms of Fields; The Isomorphism Extension Theorem; Splitting Fields; Separable Extensions; Totally Inseparable Extensions; Galois Theory; Illustrations of Galois Theory; Cyclotomic Extensions; Insolvability of the Quintic; Matrix Algebra  \u003cb\u003eMARKET: \u003c\/b\u003e For all readers interested in abstract algebra.","brand":"Pearson","offers":[{"title":"Hardcover","offer_id":47590369493143,"sku":"9780201763904","price":28154.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780201763904.webp?v=1774970012","url":"https:\/\/atlanticbooks.com\/products\/a-first-course-in-abstract-algebra-9780201763904","provider":"Atlantic Books","version":"1.0","type":"link"}