Modern Algebra: An IntroductionThe new sixth edition of Modern Algebra has two main goals: to introduce the most important kinds of algebraic structures, and to help students improve their ability to understand and work with abstract ideas. The first six chapters present the core of the subject; the remainder are designed to be as flexible as possible. The text covers groups before rings, which is a matter of personal preference for instructors. Modern Algebra, 6e is appropriate for any one-semester junior/senior level course in Modern Algebra, Abstract Algebra, Algebraic Structures, or Groups, Rings and Fields. The course is mostly comprised of mathematics majors, but engineering and computer science majors may also take it as well. |
Contents
JWCL083FM | xiv |
I | xxiii |
II | xliv |
III | 12 |
IV | 75 |
V | 106 |
xii | 120 |
VII | 137 |
X | 193 |
XI | 207 |
XII | 229 |
Solvable and Alternating Groups | 237 |
Applications of Permutation Groups | 243 |
XV | 256 |
Lattices and Boolean Algebras | 279 |
C | 304 |
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Common terms and phrases
Abelian addition algebra applied associative Assume called CHAPTER commutative Compare complete composition condition congruence Consider Construct contains Corollary corresponding cyclic defined definition denote Determine Division element equal equation equivalence relation Example exists extension fact factor field Figure Find finite Galois given gives group G group of order homomorphism ideal ideas identity element implies important integral domain INTRODUCTION inverse irreducible isomorphism JWCL083-Durbin-v2 November lattice least Lemma mapping mathematics matrix mean multiplication nonzero normal notation Notice one-to-one operation permutation plane polynomial positive integer prime Problem proof proof of Theorem properties Prove quotient rational numbers real numbers representatives respect ring root rotation SECTION solution solvable splitting field statement subfield subgroup subgroup of G subset Suggestion symmetry Theorem theory true unique unity Verify write zero