## Abstract Algebra: A First CourseThe simplicity of the language, the organization of the ideas, and the conciseness with completeness are this books main strengths as it introduces abstract algebra. It plunges directly into algebraic structures and incorporates an unusually large number of examples to clarify abstract concepts as they arise. Theorem proofs do more than just prove the stated results, they are examined so readers can gain a better impression of where the proofs come from and why they proceed as they do. Most of the exercises range from easy to moderately difficult and ask for understanding of ideas rather than flashes of insight. |

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#### Review: Abstract Algebra: A First Course

User Review - Babak - GoodreadsThis was the first book I read about group theory many years ago. It is a basic book on Group, Ring and Field Theories. But I have to say I've never seen any other book explaining the abstract ... Read full review

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addition and multiplication associative assume automorphism binary operation called coefficients commutative ring complex numbers conjugate COROLLARY cosets of H cyclic group define definition divides G element of G equivalence classes equivalence relation Euclidean domain example Exercise fact factors Fermat field finite abelian groups finite group Fundamental Theorem G and H G is abelian G is cyclic gHg~x given group and let group G group of order H in G identity element implies integral domain inverse irreducible elements isomorphic Klein's 4-group Lagrange's Theorem left cosets Lemma Let F Let G Let H mapping matrices maximal ideal nontrivial normal subgroup number of elements one-to-one permutation positive integer prime ideal PROOF real numbers right cosets ring homomorphism ring with unity Section Show that G subfield subgroup H subgroup of G subgroup of order subring Suppose Sylow subgroup Sylow Theorem trivial unique unit write zero-divisor