## Abstract AlgebraThis book includes over 1500 exercises, many with multiple parts, ranging in scope from routine to fairly sophisticated, and ranging in purpose from basic application of text material to exploration of important theoretical or computational techniques. The structure of the book permits instructors and students to pursue certain areas from their beginnings to an in-depth treatment, or to survey a wider range of areas, seeing how various themes recur and how different structures are related. The emphasis throughout has been to motivate the introduction and development of important algebraic concepts using as many examples as possible. Contains many topics not usually found in introductory texts. Students are able to see how these fit naturally into the main themes of algebra. |

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#### LibraryThing Review

User Review - rwturner - LibraryThingDummit and Foote is a nice book to own as a reference and it provides a different point of view from many other books at this level. It's not the right book to start with though; it's just too dense ... Read full review

#### Review: Abstract Algebra

User Review - Dan - GoodreadsThis book is dense and huge. So you know it has a ton of information. I don't know if it is the best treatment of the material, but it is thorough (maybe even TOO thorough.) But all in all it was the ... Read full review

### Contents

GROUP THEORY | 13 |

Subgroups | 47 |

Quotient Groups and Homomorphisms | 74 |

Copyright | |

22 other sections not shown

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### Common terms and phrases

abelian group automorphism basis bijection called coefficients cohomology commutative ring completes the proof conjugacy classes conjugate contains Corollary corresponding cosets cyclic group decomposition Deduce defined definition denote determine direct product direct sum divides element of order elementary divisors elements of G equation equivalent example field F finite group fixed follows functions functor Galois extension Galois group gives group G group of order hence identity induced injective integral domain invariant factors inverse irreducible characters isomorphic kernel left cosets Lemma Let G linear transformation matrix maximal ideal minimal polynomial module homomorphism morphism multiplication n x n nilpotent Noetherian nonzero element normal subgroup Note particular permutation prime ideal Principal Ideal Proposition Prove R-module representation ring homomorphism roots of unity Section short exact sequence Show simple group Spec splitting field subfield subgroup of G submodule subring subset Suppose surjective Sylow p-subgroup symmetric Theorem vector space Z/nZ zero