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Abstract algebra : structures and applications

Author: Stephen Lovett
Publisher: Boca Raton, FL : CRC Press, Taylor & Francis Group, [2016]
Edition/Format:   Print book : EnglishView all editions and formats
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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: 1.1. Sets and Functions --
1.2. The Cartesian Product; Operations; Relations --
1.3. Equivalence Relations --
1.4. Partial Orders --
1.5. Projects --
2.1. Basic Properties of Integers --
2.2. Modular Arithmetic --
2.3. Mathematical Induction --
2.4. Projects --
3.1. Symmetries of the Regular n-gon --
3.2. Introduction to Groups --
3.3. Properties of Group Elements --
3.4. Symmetric Groups --
3.5. Subgroups --
3.6. Lattice of Subgroups --
3.7. Group Homomorphisms --
3.8. Group Presentations --
3.9. Groups in Geometry --
3.10. Diffie-Hellman Public Key --
3.11. Semi-groups and Monoids --
3.12. Projects --
4.1. Cosets and Lagrange's Theorem --
4.2. Conjugacy and Normal Sub-groups --
4.3. Quotient Groups --
4.4. Isomorphism Theorems --
4.5. Fundamental Theorem of Finitely-Generated Abelian Groups --
4.6. Projects --
5.1. Introduction to Rings --
5.2. Rings Generated by Elements --
5.3. Matrix Rings --
5.4. Ring Homomorphisms --
5.5. Ideals --
5.6. Quotient Rings --
5.7. Maximal Ideals and Prime Ideals --
5.8. Projects --
6.1. Divisibility in Commutative Rings --
6.2. Rings of Fractions --
6.3. Euclidean Domains --
6.4. Unique Factorization Domains --
6.5. Factorization of Polynomials --
6.6. RSA Cryptography --
6.7. Algebraic Integers --
6.8. Projects --
7.1. Introduction to Field Extensions --
7.2. Algebraic Extensions --
7.3. Solving Cubic and Quartic Equations --
7.4. Constructible Numbers --
7.5. Cyclotomic Extensions --
7.6. Splitting Fields and Algebraic Closure --
7.7. Finite Fields --
7.8. Projects --
8.1. Introduction to Group Actions --
8.2. Orbits and Stabilizers --
8.3. Transitive Group Actions --
8.4. Groups Acting on Themselves --
8.5. Sylow's Theorem --
8.6. A Brief Introduction to Representations of Groups --
8.7. Projects --
9.1. Composition Series and Solvable Groups --
9.2. Finite Simple Groups --
9.3. Semi-direct Product --
9.4. Classification Theorems --
9.5. Nilpotent Groups --
9.6. Projects --
10.1. Boolean Algebras --
10.2. Vector Spaces --
10.3. Introduction to Modules --
10.4. Homomorphisms and Quotient Modules --
10.5. Free Modules and Module Decomposition --
10.6. Finitely-Generated Modules over PIDs, I --
10.7. Finitely-Generated Modules over PIDs, II --
10.8. Applications to Linear Transformations --
10.9. Jordan Canonical Form --
10.10. Applications of the Jordan Canonical Form --
10.11. A Brief Introduction to Path Algebras --
10.12. Projects --
11.1. Automorphisms of Field Extensions --
11.2. Fundamental Theorem of Galois Theory --
11.3. First Applications of Galois Theory --
11.4. Galois Groups of Cyclotomic Extensions --
11.5. Symmetries among Roots; The Discriminant --
11.6. Computing Galois Groups of Polynomials --
11.7. Fields of Finite Characteristic --
11.8. Solvability by Radicals --
11.9. Projects --
12.1. Introduction to Noetherian Rings --
12.2. Multivariable Polynomials and Affine Space --
12.3. The Nullstellensatz --
12.4. Polynomial Division; Monomial Orders --
12.5. Grobner Bases --
12.6. Buchberger's Algorithm --
12.7. Applications of Grobner Bases --
12.8. A Brief Introduction to Algebraic Geometry --
12.9. Projects --
13.1. Introduction to Categories --
13.2. Functors --
A.1. The Algebra of Complex Numbers --
A.2. Lists of Groups.
Responsibility: Stephen Lovett, Wheaton College, Wheaton, Illinois, USA.

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"... 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 Read more...

 
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