A First Graduate Course in Abstract Algebra
CRC Press, 1 févr. 2004 - 250 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.
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abelian group algebraically compact group arbitrary Artinian axiom basis bijection binary operation called characteristic value coefficients column commutative ring complex numbers composition series conjugate construct contradiction Corollary coset countable defined Definition denote direct product direct sum division ring easy to check element embedding epimorphism equation equivalence class equivalence relation exact sequence Example Exercise extension of F factor group factor set field F finite abelian groups finite dimensional function Galois group group G group of order Hence ideal ofR identity induction inner product integers inverse irreducible in Q[x left ideals Let G linear transformation matrix maximal minimal polynomial module monic natural number nonzero normal subgroup notation p-group Problem Set Problem proof is complete Prove R-module scalar simple splitting field structure theorem subfield subgroup of G submodule subring subset subspace Suppose Sylow p-subgroup Sylow Theorems tensor Theory torsion-free unique vector space write Z/pZ zero