SolutionsHungerfordPart1

SolutionsHungerfordPart1 - A Hungerfords Algebra Solutions...

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Unformatted text preview: A Hungerfords Algebra Solutions Manual Volume I: Introduction through Chapter IV James Wilson I D 4 h a 2 ,b i h a i h a 2 ,ab i h b i h a 2 b i h a 2 i h ab i h a 3 b i- C--------- C-------------- II = C ( G ) C 1 ( G ) C n- 1 ( G ) C n ( G ) = G = G n G n- 1 G 1 G = G = n +1 G n G 2 G 1 G = G = = III Commutative Ring Local Ring Field Integral Domain Unique Factorization Domain Ring Unital Ring Principal Ideal Domain Skew Field Principal Ideal Ring Euclidean Domain Euclidean Ring--------------------------------------------------------- IV A B C A B C Published: April 20, 2003 c 2002-2003. James Wilson University of Oregon, Portland State University. 3234 SE Spruce St. Hillsboro OR 97123 James.Wilson@scatter.com Written with L A T E X2 . Please Recycle when finished. Contents Prerequisites and Preliminaries 11 .7 The Axiom of Choice, Order and Zorns Lemma . . . . . . . . . . 11 .7.1 Lattice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 .7.2 Complete. . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 .7.3 Well-ordering. . . . . . . . . . . . . . . . . . . . . . . . . . 13 .7.4 Choice Function. . . . . . . . . . . . . . . . . . . . . . . . 14 .7.5 Semi-Lexicographic Order. . . . . . . . . . . . . . . . . . 14 .7.6 Projections. . . . . . . . . . . . . . . . . . . . . . . . . . . 15 .7.7 Successors. . . . . . . . . . . . . . . . . . . . . . . . . . . 15 .8 Cardinal Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 17 .8.1 Pigeon-Hole Principle. . . . . . . . . . . . . . . . . . . . . 17 .8.2 Cardinality. . . . . . . . . . . . . . . . . . . . . . . . . . . 18 .8.3 Countable. . . . . . . . . . . . . . . . . . . . . . . . . . . 19 .8.4 Cardinal Arithmetic. . . . . . . . . . . . . . . . . . . . . . 19 .8.5 Cardinal Arithmetic Properties. . . . . . . . . . . . . . . . 20 .8.6 Finite Cardinal Arithmetic. . . . . . . . . . . . . . . . . . . 21 .8.7 Cardinal Order. . . . . . . . . . . . . . . . . . . . . . . . . 22 .8.8 Countable Subsets. . . . . . . . . . . . . . . . . . . . . . 22 .8.9 Cantors Diagonalization Method. . . . . . . . . . . . . . . 23 .8.10 Cardinal Exponents. . . . . . . . . . . . . . . . . . . . . . 23 .8.11 Unions of Finite Sets. . . . . . . . . . . . . . . . . . . . . 25 .8.12 Fixed Cardinal Unions. . . . . . . . . . . . . . . . . . . . . 26 I Groups 27 I.1 Semigroups, Monoids, and Groups . . . . . . . . . . . . . . . . . 27 I.1.1 Non-group Objects. . . . . . . . . . . . . . . . . . . . . . 27 I.1.2 Groups of Functions. . . . . . . . . . . . . . . . . . . . . . 28 I.1.3 Floops. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 I.1.4 D 4 Table. . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 I.1.5 Order of S n . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 I.1.6 Klein Four Group. . . . . . . . . . . . . . . . . . . . . . . 29 I.1.7 Z...
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This note was uploaded on 04/06/2010 for the course MATH various taught by Professor Tao/analysis during the Spring '10 term at UCLA.

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SolutionsHungerfordPart1 - A Hungerfords Algebra Solutions...

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