A first course in abstract algebra :
Anderson, Marlow, 1950-
A first course in abstract algebra : rings, groups, and fields / Marlow Anderson, Todd Feil. - 2nd ed. - Boca Raton : Chapman & Hall/CRC, c2005. - xviii, 673 p. : ill. ; 25 cm.
Includes index.
The natural numbers -- The integers -- Modular arithmetic -- Polynomials with rational coefficients -- Factorization of polynomials -- Rings -- Subrings and unity -- Integral domains and fields -- Polynomials over a field -- Associates and irreducibles -- Factorization and ideals -- Principal ideal domains -- Primes and unique factorization -- Polynomials with integer coefficients -- Euclidean domains -- Ring homomorphisms -- The kernel -- Rings of cosets -- The isomorphism theorem for rings -- Maximal and prime ideals -- The Chinese remainder theorem -- Symmetries of figures in the plane -- Symmetries of figures in space -- Abstract groups -- Subgroups -- Cyclic groups -- Group homomorphisms -- Group isomorphisms -- Permutations and Cayley's theorem -- More about permutations -- Cosets and Lagrange's theorem -- Groups of cosets -- The isomorphism theorem for groups -- The alternating groups -- Fundamental theorem for finite Abelian groups -- Solvable groups -- Constructions with compass and straightedge -- Constructibility and quadratic field extensions -- The impossibility of certain constructions -- Vector spaces I -- Vector spaces II -- Field extensions and Kronecker's theorem -- Algebraic field extensions -- Finite extensions and constructibility revisited -- The splitting field -- Finite fields -- Galois groups -- The fundamental theorem of Galois theory -- Solving polynomials by radicals. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.
"As stated in the title, this book is designed for a first course. It requires only a typical calculus sequence as a prerequisite and does not assume any familiarity with linear algebra or complex number."--BOOK JACKET.
1584885157 (alk. paper)
2004061805
Algebra, Abstract.
QA162 / .A53 2005
512/.02
A first course in abstract algebra : rings, groups, and fields / Marlow Anderson, Todd Feil. - 2nd ed. - Boca Raton : Chapman & Hall/CRC, c2005. - xviii, 673 p. : ill. ; 25 cm.
Includes index.
The natural numbers -- The integers -- Modular arithmetic -- Polynomials with rational coefficients -- Factorization of polynomials -- Rings -- Subrings and unity -- Integral domains and fields -- Polynomials over a field -- Associates and irreducibles -- Factorization and ideals -- Principal ideal domains -- Primes and unique factorization -- Polynomials with integer coefficients -- Euclidean domains -- Ring homomorphisms -- The kernel -- Rings of cosets -- The isomorphism theorem for rings -- Maximal and prime ideals -- The Chinese remainder theorem -- Symmetries of figures in the plane -- Symmetries of figures in space -- Abstract groups -- Subgroups -- Cyclic groups -- Group homomorphisms -- Group isomorphisms -- Permutations and Cayley's theorem -- More about permutations -- Cosets and Lagrange's theorem -- Groups of cosets -- The isomorphism theorem for groups -- The alternating groups -- Fundamental theorem for finite Abelian groups -- Solvable groups -- Constructions with compass and straightedge -- Constructibility and quadratic field extensions -- The impossibility of certain constructions -- Vector spaces I -- Vector spaces II -- Field extensions and Kronecker's theorem -- Algebraic field extensions -- Finite extensions and constructibility revisited -- The splitting field -- Finite fields -- Galois groups -- The fundamental theorem of Galois theory -- Solving polynomials by radicals. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49.
"As stated in the title, this book is designed for a first course. It requires only a typical calculus sequence as a prerequisite and does not assume any familiarity with linear algebra or complex number."--BOOK JACKET.
1584885157 (alk. paper)
2004061805
Algebra, Abstract.
QA162 / .A53 2005
512/.02