This textual content introduces readers to the algebraic ideas of group and rings, offering a complete dialogue of concept in addition to a big variety of purposes for every. Download First Course in Abstract Algebra Guide pdf in free.

KEY TOPICS: Quantity Concept: Induction; Binomial Coefficients; Best Widespread Divisors; The Elementary Theorem of Arithmetic Congruences; Dates and Days.

Book Description:

This text introduces readers to the algebraic concepts of group and rings, providing a comprehensive discussion of theory as well as a significant number of applications for each. Number Theory: Induction; Binomial Coefficients; Greatest Common Divisors; The Fundamental Theorem of Arithmetic Congruences; Dates and Days. Groups I: Some Set Theory; Permutations; Groups; Subgroups and Lagrange’s Theorem; Homomorphisms; Quotient Groups; Group Actions; Counting with Groups.Commutative Rings I: First Properties; Fields; Polynomials; Homomorphisms; Greatest Common Divisors; Unique Factorization; Irreducibility; Quotient Rings and Finite Fields; Officers, Magic, Fertilizer, and Horizons.Linear Algebra: Vector Spaces; Euclidean Constructions; Linear Transformations; Determinants; Codes; Canonical Forms.Fields: Classical Formulas; Insolvability of the General Quintic; Epilog. Groups II: Finite Abelian Groups; The Sylow Theorems; Ornamental Symmetry. Commutative Rings III: Prime Ideals and Maximal Ideals; Unique Factorization; Noetherian Rings; Varieties; Grobner Bases. For all readers interested in abstract algebra.

A First Course in Abstract Algebra: With Applications [3 ed.]

Author(s): Joseph J. Rotman

Publisher: Pearson Prentice Hall

Year: 2005

ISBN: 0131862677

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