A First Graduate Course in Abstract AlgebraCRC Press, 27 sept. 2019 - 232 pages Since abstract algebra is so important to the study of advanced mathematics, it is critical that students have a firm grasp of its principles and underlying theories before moving on to further study. To accomplish this, they require a concise, accessible, user-friendly textbook that is both challenging and stimulating. A First Graduate Course in Abstract Algebra is just such a textbook.Divided into two sections, this book covers both the standard topics (groups, modules, rings, and vector spaces) associated with abstract algebra and more advanced topics such as Galois fields, noncommutative rings, group extensions, and Abelian groups. The author includes review material where needed instead of in a single chapter, giving convenient access with minimal page turning. He also provides ample examples, exercises, and problem sets to reinforce the material. This book illustrates the theory of finitely generated modules over principal ideal domains, discusses tensor products, and demonstrates the development of determinants. It also covers Sylow theory and Jordan canonical form.A First Graduate Course in Abstract Algebra is ideal for a two-semester course, providing enough examples, problems, and exercises for a deep understanding. Each of the final three chapters is logically independent and can be covered in any order, perfect for a customized syllabus. |
Table des matières
Chapter 1 Groups mostly finite | 1 |
Chapter 2 Rings mostly domains | 41 |
Chapter 3 Modules | 62 |
Chapter 4 Vector spaces | 80 |
Chapter 5 Fields and Galois theory | 124 |
Chapter 6 Topics in Noncommutative Rings | 152 |
Chapter 7 Group extensions | 166 |
Chapter 8 Topics in abelian groups | 179 |
References | 200 |
201 | |
Autres éditions - Tout afficher
Expressions et termes fréquents
abelian group additive algebraic apply associative axiom basis called Chapter characteristic claim closed column commutative complete consider construct contains contradiction Corollary corresponding cyclic defined Definition denote determinant direct sum distinct divides divisible domain easy element embedding equal equation equivalence Example Exercise exists extension fact factor Finally Find finite fixed follows formula function give given group G Hence homomorphism ideal identity independent induction integers invariant inverse irreducible isomorphism Lemma linear matrix maximal module multiplication natural nonzero Note obtain operator polynomial positive prime Problem Problem Set Problem proof proof is complete proper Prove R-module relation respect result ring root sequence simple solvable splitting field standard structure subfield subgroup submodule subset summand Suppose Theorem Theory unique unit vector space write written zero