A first course in abstract algebra : with applications

Joseph J. Rotman

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.

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  • Chapter 1: Number Theory Induction Binomial Coefficients Greatest Common Divisors The Fundamental Theorem of Arithmetic Congruences Dates and Days Chapter 2: Groups I Some Set Theory Permutations Groups Subgroups and Lagrange's Theorem Homomorphisms Quotient Groups Group Actions Counting with Groups Chapter 3: Commutative Rings I First Properties Fields Polynomials Homomorphisms Greatest Common Divisors Unique Factorization Irreducibility Quotient Rings and Finite Fields Officers, Magic, Fertilizer, and Horizons Chapter 4: Linear Algebra Vector Spaces Euclidean Constructions Linear Transformations Determinants Codes Canonical Forms Chapter 5: Fields Classical Formulas Insolvability of the General Quintic Epilog Chapter 6: Groups II Finite Abelian Groups The Sylow Theorems Ornamental Symmetry Chapter 7: Commutative Rings III Prime Ideals and Maximal Ideals Unique Factorization Noetherian Rings Varieties Grobner Bases Hints for Selected Exercises Bibliography Index

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書名 A first course in abstract algebra : with applications
著作者等 Rotman, Joseph J.
出版元 Pearson Prentice Hall
刊行年月 c2006
版表示 3rd ed
ページ数 1 v.
大きさ 24 cm
ISBN 0131862677
NCID BB17745709
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言語 英語
出版国 アメリカ合衆国