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## Details

Genre/Form: | Textbooks |
---|---|

Document Type: | Book |

All Authors / Contributors: |
Stephen Lovett |

ISBN: | 9781482248906 1482248905 |

OCLC Number: | 903812715 |

Notes: | "A Chapman & Hall book." |

Description: | xii, 708 pages : illustrations ; 29 cm |

Contents: | SET THEORY Sets and Functions The Cartesian Product; Operations; Relations Equivalence Relations Partial Orders NUMBER THEORY Basic Properties of Integers Modular Arithmetic Mathematical Induction GROUPS Symmetries of the Regular n-gon Introduction to Groups Properties of Group Elements Symmetric Groups Subgroups Lattice of Subgroups Group Homomorphisms Group Presentations Groups in Geometry Diffie-Hellman Public Key Semigroups and Monoids QUOTIENT GROUPS Cosets and Lagrange's Theorem Conjugacy and Normal Subgroups Quotient Groups Isomorphism Theorems Fundamental Theorem of Finitely Generated Abelian Groups RINGS Introduction to Rings Rings Generated by Elements Matrix Rings Ring Homomorphisms Ideals Quotient Rings Maximal and Prime Ideals DIVISIBILITY IN COMMUTATIVE RINGS Divisibility in Commutative Rings Rings of Fractions Euclidean Domains Unique Factorization Domains Factorization of Polynomials RSA Cryptography Algebraic Integers FIELD EXTENSIONS Introduction to Field Extensions Algebraic Extensions Solving Cubic and Quartic Equations Constructible Numbers Cyclotomic Extensions Splitting Fields and Algebraic Closures Finite Fields GROUP ACTIONS Introduction to Group Actions Orbits and Stabilizers Transitive Group Actions Groups Acting on Themselves Sylow's Theorem A Brief Introduction to Representations of Groups CLASSIFICATION OF GROUPS Composition Series and Solvable Groups Finite Simple Groups Semidirect Product. Classification Theorems Nilpotent Groups MODULES AND ALGEBRAS Boolean Algebras Vector Spaces Introduction to Modules Homomorphisms and Quotient Modules Free Modules and Module Decomposition Finitely Generated Modules over PIDs, I Finitely Generated Modules over PIDs, II Applications to Linear Transformations Jordan Canonical Form Applications of the Jordan Canonical Form A Brief Introduction to Path Algebras GALOIS THEORY Automorphisms of Field Extensions Fundamental Theorem of Galois Theory First Applications of Galois Theory Galois Groups of Cyclotomic Extensions Symmetries among Roots; The Discriminant Computing Galois Groups of Polynomials Fields of Finite Characteristic Solvability by Radicals MULTIVARIABLE POLYNOMIAL RINGS Introduction to Noetherian Rings Multivariable Polynomial Rings and Affine Space The Nullstellensatz Polynomial Division; Monomial Orders Grobner Bases Buchberger's Algorithm Applications of Grobner Bases A Brief Introduction to Algebraic Geometry CATEGORIES Introduction to Categories Functors APPENDICES LIST OF NOTATIONS BIBLIOGRAPHY INDEX Projects appear at the end of each chapter. |

Responsibility: | Stephen Lovett, Wheaton College, Wheaton, Illinois, USA. |

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## Reviews

*Editorial reviews*

Publisher Synopsis

"... lucid, detailed, and versatile main text comes with a wealth of illustrating examples and very instructive exercises in each single section of the book, and each chapter ends with a section containing project ideas (and hints) to challenge the student to write her or his own investigative or expository papers on related topics. ... an excellent introduction to the principles of abstract algebra for upper undergraduate and graduate students, and a valuable source for instructors likewise. No doubt, this text is a highly welcome addition to the already existing plethora of primers on abstract algebra in the mathematical literature." -Zentralblatt MATH 1323 "This is a text for a serious upper-level undergraduate course in abstract algebra. It adopts a 'groups first' approach to the subject, and, although it starts from scratch, winds up covering more than enough material to fill out two semesters. The topic coverage is very extensive for an undergraduate text ... The author does an excellent job of balancing theory with applications. ... The inclusion of all the topics described above and the large number of exercises, examples and projects make for an undeniably interesting text ... a well-written book with interesting features ... " -MAA Reviews, November 2015 Read more...

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