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Preface.... ..7 Chapter 1. Sets and Binary Relations..9 1.1 Sets. 9 1.2 Binary Relations. 1 3 1.3 Functions .. 16 1.4 Order Relations. .. 2 0 1.5 Boolean Matrices and Graphs...26 1.6 Arrow’s Impossibility Theorem. 3 2 Chapter 2. Semigroups and Groups...39 2.1 Semigroups ..40 2.2 Generators and Relations. 4 4 2.3 Green’s Relations. 5 0 2.4 Blockmodels. . ..55 2.5 Finite State Machines. 6 0 2.6 Recognition of Machine Languages by Finite State Machines. 6 3 2.7 Groups. .67 2.8 Subgroups.72 2.9 Homomorphisms. 7 6 2.10 Permutation Groups. . ..79 2.11 Systems of Distinct Representatives and Flows on Networks.83 2.12 Orbits and Conjugations. 9 2 2.13 Symmetries.98 2.14 Polya Enumeration.107 2.15 Kinship Systems. I ll 2.16 Lattices of Subgroups ..114 Chapter 3. Vector Spaces.119 3.1 Vector Spaces.120 3.2 Basis and Dimension.126 3.3 Matrices.131 3.4 Linear Transformations.138 3.5 Determinants and Characteristic Polynomials.143 3.6 Eigenvalues, Eigenvectors, Similarity.149 3.7 Symmetric and Unitary Matrices.157 Chapter 4. Rings.163 4.1 The Integers and Divisibility.164 4.2 Euclidean Domains and Factorization.168 4.3 Ideals and Congruences.173 4.4 Structure of Z n . 1 7 6 4.5 Simple and Semis

Who reads Applied abstract algebra (Ellis Horwood series in mathematics and its applications)?

Author

Ki Hang Kim, Fred William Roush

Publisher

Ellis Horwood Limited & Halsted Press & Wiley

Published

1983

Language

EN

ISBN

9780853125631

Category

mathematics

Subjects

Mathematics, Algebra, Stem

Updated

2026-03-25