## Abstract Algebra Manual: Problems and SolutionsThis is the most current textbook in teaching the basic concepts of abstract algebra. The author finds that there are many students who just memorise a theorem without having the ability to apply it to a given problem. Therefore, this is a hands-on manual, where many typical algebraic problems are provided for students to be able to apply the theorems and to actually practice the methods they have learned. Each chapter begins with a statement of a major result in Group and Ring Theory, followed by problems and solutions. Contents: Tools and Major Results of Groups; Problems in Group Theory; Tools and Major Results of Ring Theory; Problems in Ring Theory; Index. |

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sir, i have gone through this book .i am in chennai . In which shop in chennai i get this book,pls reply

### Contents

Tools and Major Results of Groups | 1 |

12 Results | 2 |

Problems in Group Theory | 9 |

22 Subgroups | 13 |

23 Cyclic Groups | 16 |

24 Permutation Groups | 20 |

25 Cosets and Lagranges Theorem | 24 |

26 Normal Subgroups and Factor Groups | 30 |

Problems in Ring Theory | 67 |

42 Ideals Subrings and Factor Rings | 71 |

43 Integral Domains and Zero Divisors | 79 |

44 Ring Homomorphisms and Ideals | 83 |

45 Polynomial Rings | 91 |

46 Factorization in Polynomial Rings | 97 |

47 Extension Fields and Algebraic Fields | 100 |

48 Finite Fields | 105 |

27 Group Homomorphisms and Direct Product | 37 |

28 Sylow Theorems | 50 |

Tools and Major Results of Ring Theory | 59 |

32 Major Results of Ring Theory | 60 |

113 | |

115 | |

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2-cycles A'er Abelian group C F[x Char(A commutative ring conclude that f(x conclude that H contradiction cyclic group deg(f(x divides Ord(G E F[x elements in G elements of order extension field finite field finite group G by Theorem g C G G contains G is Abelian G is cyclic G of order g~lHg gcd(n,m GF(pn group G group homomorphism group of order H in G H is normal Hence ideal of Z[x infinite integral domain irreducible over Q irreducible polynomial left cosets Let F Let f(x Let G Let H maximal ideal normal in G normal subgroup number of elements odd number Ord(a Ord(b Ord(H Ord(Ker Ord(Z(G positive integer previous Question prime ideal prime maximal prime number proper subgroup Prove that G Question we conclude ring homomorphism roots zeros Solution splitting field subgroup of G subgroup of order subring Sylow p-subgroup Zero divisors