A book of abstract algebra
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York u.a.
McGraw-Hill
1990
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| Ausgabe: | 2. ed. |
| Schriftenreihe: | International series inpure and applied mathematics
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| Online-Zugang: | Inhaltsverzeichnis |
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| 100 | 1 | |a Pinter, Charles C. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a A book of abstract algebra |c Charles C. Pinter |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York u.a. |b McGraw-Hill |c 1990 | |
| 300 | |a XVIII, 384 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a International series inpure and applied mathematics | |
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Datensatz im Suchindex
| _version_ | 1804118617784057856 |
|---|---|
| adam_text | A BOOK OF
ABSTRACT ALGEBRA
Second Edition
Charles C Pinter
Professor of Mathematics
Bucknell University
McGraw-Hill Publishing Company
New York St Louis San Francisco Auckland Bogota Caracas Hamburg
Lisbon London Madrid Mexico Milan Montreal New Delhi Oklahoma City
Paris San Juan Sao Paulo Singapore Sydney Tokyo Toronto
CONTENTS*
Preface xv
Chapter 1 Why Abstract Algebra? l
History of Algebra New Algebras Algebraic
Structures Axioms and Axiomatic Algebra
Abstraction in Algebra
Chapter 2 Operat ions 19
Operations on a Set Properties of Operations
Chapter 3 The Definition of Groups 25
Groups Examples of Infinite and Finite Groups
Examples of Abelian and Nonabelian Groups
Group Tables
Theory of Coding: Maximum-Likelihood Decoding
Chapter 4 Elementary Properties of Groups 36
Uniqueness of Identity and Inverses Properties
of Inverses
Direct Product of Groups
Chapter 5 Subgroups 44
Definition of Subgroup Generators and Defining
Relations
Cayley Diagrams Center of a Group Group Codes;
Hamming Code
* Italic headings indicate topics discussed in the exercise sections
X CONTENTS
Chapter 6 Functions 56
Injective, Surjective, Bijective Function Composite
and Inverse of Functions
Finite-State Machines Automata and Their Semigroups
Chapter 7 Groups of Permutations 69
Symmetric Groups Dihedral Groups
An Application of Groups to Anthropology
Chapter 8 Permutations of a Finite Set 80
Decomposition of Permutations into Cycles
Transpositions Even and Odd Permutations
Alternating Groups
Chapter 9 Isomorphism 90
The Concept of Isomorphism in Mathematics
Isomorphic and Nonisomorphic Groups
Cayley s Theorem
Group Automorphisms
Chapter 10 O rde r pf G r oup E lements 103
Powers/Multiples of Group Elements Laws of
Exponents Properties of the Order of Group
Elements
Chapter 11 Cyclic Groups 112
Finite and Infinite Cyclic Groups Isomorphism
of Cyclic Groups Subgroups of Cyclic Groups
Chapter 12 Part i t ions and Equivalence Relat ions 119
Chapter 13 Count ing Cosets 126
Lagrange s Theorem and Elementary Consequences
Survey of Groups of Order s 10
Number of Conjugate Elements Group Acting on a Set
Chapter 14 Homomorph i sms 136
Elementary Properties of Homomorphisms Normal
Subgroups Kernel and Range
Inner Direct Products Conjugate Subgroups
CONTENTS
Chapter 15 Quotient Groups 147
Quotient Group Construction Examples and
Applications
The Class Equation Induction on the Order of a Group
Chapter 16 The Fundamental Homomorphism
Theorem 157
Fundamental Homomorphism Theorem and Some
Consequences
The Isomorphism Theorems The Correspondence Theorem
Cauchy s Theorem Sylow Subgroups Sylow s Theorem
Decomposition Theorem for Finite Abelian Groups
Chapter 17 Rings: Definitions and
Elementary Properties 169
Commutative Rings Unity Invertibles and
Zero-Divisors Integral Domain Field
Chapter 18 Ideals and Homomorphisms 181
Chapter 19 Quotient Rings
Construction of Quotient Rings Examples
Fundamental Homomorphism Theorem and Some
Consequences Properties of Prime and Maximal
Ideals
Chapter 20 Integral Domains
Characteristic of an Integral Domain Properties
of the Characteristic Finite Fields Construction
of the Field of Quotients
Chapter 21 The Integers
Ordered Integral Domains Well-ordering
Characterization of Z Up to Isomorphism
Induction Division Algorithm
Mathematical
Chapter 22 Factoring into Primes
Ideals of Z Properties of the GCD Relatively
Prime Integers Primes Euclid s Lemma Unique
Factorization
Xii CONTENTS
Chapter 23 Elements of Number Theory (Optional)
Properties of Congruence Theorems of Fermat and
Euler Solutions of Linear Congruences Chinese
Remainder Theorem
Wilson s Theorem and Consequences Quadratic Residues
The Legendre Symbol Primitive Roots
Chapter 24 Rings of Polynomials 240
Motivation and Definitions Domain of Polynomials
over a Field Division Algorithm
Polynomials in Several Variables Fields of Polynomial Quotients
Chapter 25 Factoring Polynomials
Ideals of F[x] Properties of the GCD Irreducible
Polynomials Unique factorization
Euclidean Algorithm
Chapter 26 Substitution in Polynomials
Roots and Factors Polynomial Functions
Polynomials over Q Eisenstein s Irreducibility
Criterion Polynomials over the Reals Polynomial
Interpolation
Chapter 27 Extensions of Fields
Algebraic and Transcendental Elements The
Minimum Polynomial Basic Theorem on Field
Extensions
Chapter 28 Vector Spaces
Elementary Properties of Vector Spaces Linear
Independence Basis Dimension Linear
Transformations
Chapter 29 Degrees of Field Extensions 292
Simple and Iterated Extensions Degree of an Iterated
Extension
Fields of Algebraic Elements Algebraic Numbers Algebraic
Closure
CONTENTS Xiii
Chapter 30 Ruler and Compass 301
Constructive Points and Numbers Impossible
Constructions
Constructive Angles and Polygons
Chapter 31 Galois Theory: Preamble 311
Multiple Roots Root Field Extension of a Field
Isomorphism
Roots of Unity Separable Polynomials Normal Extensions
Chapter 32 Galois Theory: The Heart of the Matter 323
Field Automorphisms The Galois Group The
Galois Correspondence Fundamental Theorem of
Galois Theory
Computing Galois Groups
Chapter 33 Solving Equations by Radicals 334
Radical Extensions Abelian Extensions Solvable
Groups Insolvability of the Quintic
Appendix A Review of Set Theory 345
Appendix B Review of the Integers 349
Appendix C Review of Mathematical Induction
Answers to Selected Exercises 353
Index - 381
|
| any_adam_object | 1 |
| author | Pinter, Charles C. |
| author_facet | Pinter, Charles C. |
| author_role | aut |
| author_sort | Pinter, Charles C. |
| author_variant | c c p cc ccp |
| building | Verbundindex |
| bvnumber | BV004444931 |
| classification_rvk | SK 200 |
| classification_tum | MAT 110f |
| ctrlnum | (OCoLC)300306985 (DE-599)BVBBV004444931 |
| discipline | Mathematik |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV004444931 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:13:09Z |
| institution | BVB |
| isbn | 0070501386 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002757414 |
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| physical | XVIII, 384 S. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | McGraw-Hill |
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| series2 | International series inpure and applied mathematics |
| spelling | Pinter, Charles C. Verfasser aut A book of abstract algebra Charles C. Pinter 2. ed. New York u.a. McGraw-Hill 1990 XVIII, 384 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier International series inpure and applied mathematics Universelle Algebra (DE-588)4061777-4 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Algebra (DE-588)4001156-2 s DE-604 Universelle Algebra (DE-588)4061777-4 s DE-188 HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002757414&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Pinter, Charles C. A book of abstract algebra Universelle Algebra (DE-588)4061777-4 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4061777-4 (DE-588)4001156-2 (DE-588)4123623-3 |
| title | A book of abstract algebra |
| title_auth | A book of abstract algebra |
| title_exact_search | A book of abstract algebra |
| title_full | A book of abstract algebra Charles C. Pinter |
| title_fullStr | A book of abstract algebra Charles C. Pinter |
| title_full_unstemmed | A book of abstract algebra Charles C. Pinter |
| title_short | A book of abstract algebra |
| title_sort | a book of abstract algebra |
| topic | Universelle Algebra (DE-588)4061777-4 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Universelle Algebra Algebra Lehrbuch |
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