TY  - BOOK
AU  - Anderson,Marlow
AU  - Feil,Todd
TI  - First course in abstract algebra: rings, groups, and fields 
SN  - 9781482245523 (hardcover : alk. paper)
U1  - 512.02 23
PY  - 2015///
CY  - Boca Raton :       
PB  - CRC Press
KW  - Abstract Algebra
N1  - Includes index; Chapter 1: The Natural Numbers; 
Chapter 2: The Integers; 
Chapter 3: Modular Arithmetic; 
Chapter 4: Polynomials with Rational Coefficients; 
Chapter 5: Factorization of Polynomials; 
Section I: in a Nutshell; 
Part II: Rings, Domains, and Fields; 
Chapter 6: Rings; 
Chapter 7: Subrings and Unity; 
Chapter 8: Integral Domains and Fields; 
Chapter 9: Ideals; 
Chapter 10: Polynomials over a Field; 
Section II: in a Nutshell; 
Part III: Ring Homomorphisms and Ideals; 
Chapter 11: Ring Homomorphisms; 
Chapter 12: The Kernel; 
Chapter 13: Rings of Cosets;
Chapter 14: The Isomorphism Theorem for Rings; 
Chapter 15: Maximal and Prime Ideals; 
Chapter 16: The Chinese Remainder Theorem; 
Section III: in a Nutshell; 
Part IV: Groups; 
Chapter 17: Symmetries of Geometric Figures; 
Chapter 18: Permutations; 
Chapter 19: Abstract Groups; 
Chapter 20: Subgroups; 
Chapter 21: Cyclic Groups; 
Section IV: in a Nutshell; 
Part V: Group Homomorphisms; 
Chapter 22: Group Homomorphisms; 
Chapter 23: Structure and Representation; 
Chapter 24: Cosets and Lagrange's Theorem; 
Chapter 25: Groups of Cosets; 
Chapter 26: The Isomorphism Theorem for Groups;
Section V: in a Nutshell; 
Part VI: Topics from Group Theory; 
Chapter 27: The Alternating Groups; 
Chapter 28: Sylow Theory: The Preliminaries; 
Chapter 29: Sylow Theory: The Theorems; 
Chapter 30: Solvable Groups; 
Section VI: in a Nutshell; 
Part VII: Unique Factorization; 
Chapter 31: Quadratic Extensions of the Integers; 
Chapter 32: Factorization; 
Chapter 33: Unique Factorization; 
Chapter 34: Polynomials with Integer Coefficients; 
Chapter 35: Euclidean Domains; 
Section VII: in a Nutshell; 
Part VIII: Constructibility Problems;
Chapter 36: Constructions with Compass and Straightedge;
Chapter 37: Constructibility and Quadratic Field Extensions; Chapter 38: The Impossibility of Certain Constructions; 
Section VIII: in a Nutshell; 
Part IX: Vector Spaces and Field Extensions; 
Chapter 39: Vector Spaces I; 
Chapter 40: Vector Spaces II; 
Chapter 41: Field Extensions and Kronecker's Theorem; Chapter 42: Algebraic Field Extensions; 
Chapter 43: Finite Extensions and Constructibility Revisited; Section IX: in a Nutshell; Part X: Galois Theory; 
Chapter 44: The Splitting Field; 
Chapter 45: Finite Fields; 
Chapter 46: Galois Groups; 
Chapter 47: The Fundamental Theorem of Galois Theory;
Chapter 48: Solving Polynomials by Radicals; 
Section X: in a Nutshell; 
Hints and Solutions; 
Guide to Notation;
Indes
N2  - The text includes straightforward exercises within each chapter for students to quickly verify facts, warm-up exercises following the chapter that test fundamental comprehension, and regular exercises concluding the chapter that consist of computational and supply-the-proof problems. Historical remarks discuss the history of algebra to underscore certain pedagogical points. Each section also provides a synopsis that presents important definitions and theorems, allowing students to verify the major topics from the section.

ER  -