MTU Library Catalogue

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A first course in abstract algebra / Joseph J. Rotman.

By: Rotman, Joseph J, 1934-.
Material type: materialTypeLabelBookPublisher: Upper Saddle River, N.J. : Prentice Hall, c1996Description: xi, 265 p.. : ill. ; 24 cm. + hbk.ISBN: 0133113744.Subject(s): Algebra, AbstractDDC classification: 512.02
Contents:
Number theory -- Groups -- Commutative rings -- Goodies.
Holdings
Item type Current library Call number Copy number Status Barcode
General lending MTU Bishopstown Library Lending 512.02 (Browse shelf(Opens below)) 1 Available 00069064
Total holds: 0

Enhanced descriptions from Syndetics:

This undergraduate text in abstract algebra aims to present difficult material in an accessible way.

Bibliography: (page 258) and index.

Number theory -- Groups -- Commutative rings -- Goodies.

Table of contents provided by Syndetics

  • Preface to the First Edition (p. vii)
  • Preface to the Second Edition (p. xi)
  • Chapter 1 Number Theory (p. 1)
  • 1.1. Induction (p. 1)
  • 1.2. Binomial Coefficients (p. 17)
  • 1.3. Greatest Common Divisors (p. 36)
  • 1.4. The Fundamental Theorem of Arithmetic (p. 58)
  • 1.5. Congruences (p. 62)
  • 1.6. Dates and Days (p. 73)
  • Chapter 2 Groups I (p. 82)
  • 2.1. Functions (p. 82)
  • 2.2. Permutations (p. 97)
  • 2.3. Groups (p. 115)
  • Symmetry (p. 128)
  • 2.4. Lagrange's Theorem (p. 134)
  • 2.5. Homomorphisms (p. 143)
  • 2.6. Quotient Groups (p. 156)
  • 2.7. Group Actions (p. 178)
  • 2.8. Counting with Groups (p. 194)
  • Chapter 3 Commutative Rings I (p. 203)
  • 3.1. First Properties (p. 203)
  • 3.2. Fields (p. 216)
  • 3.3. Polynomials (p. 225)
  • 3.4. Homomorphisms (p. 233)
  • 3.5. Greatest Common Divisors (p. 239)
  • Euclidean Rings (p. 252)
  • 3.6. Unique Factorization (p. 261)
  • 3.7. Irreducibility (p. 267)
  • 3.8. Quotient Rings and Finite Fields (p. 278)
  • 3.9. Officers, Fertilizer, and a Line at Infinity (p. 289)
  • Chapter 4 Goodies (p. 301)
  • 4.1. Linear Algebra (p. 301)
  • Vector Spaces (p. 301)
  • Linear Transformations (p. 318)
  • Applications to Fields (p. 329)
  • 4.2. Euclidean Constructions (p. 332)
  • 4.3. Classical Formulas (p. 345)
  • 4.4. Insolvability of the General Quintic (p. 363)
  • Formulas and Solvability by Radicals (p. 368)
  • Translation into Group Theory (p. 371)
  • 4.5. Epilog (p. 381)
  • Chapter 5 Groups II (p. 385)
  • 5.1. Finite Abelian Groups (p. 385)
  • 5.2. The Sylow Theorems (p. 397)
  • 5.3. The Jordan-Holder Theorem (p. 408)
  • 5.4. Presentations (p. 420)
  • Chapter 6 Commutative Rings II (p. 437)
  • 6.1. Prime Ideals and Maximal Ideals (p. 437)
  • 6.2. Unique Factorization (p. 445)
  • 6.3. Noetherian Rings (p. 456)
  • 6.4. Varieties (p. 462)
  • 6.5. Grobner Bases (p. 480)
  • Generalized Division Algorithm (p. 482)
  • Grobner Bases (p. 493)
  • Hints to Exercises (p. 505)
  • Bibliography (p. 519)
  • Index (p. 521)