Abstract algebra - Saracino, Dan, 1947- (London : ED-Tech Press, 2023)
The book preserved the emphasis on providing a large number of examples and on helping students learn how to write proofs. The presentation of the sections is given at a higher level. Unusual features, for a book is still relatively short, are the inclusion of full proofs of both directions of Gauss' theorem on constructible regular polygons and Galois' theorem on solvability by radicals, a Galois-theoretic proof of the Fundamental Theorem of Algebra, and a proof of the Primitive Element Theorem. The changes include the simplification of some points in the addition of some new exercise, and the updating of some historical material. All the topics are given in step by step method with simple language to understand the concept easily. This book is intended for use in a junior-senior level course in abstract algebra.
Sets and induction ; Binary operations ; Groups ; Fundamental theorems about groups ; Powers of an element; cyclic groups ; Subgroups ; Direct products ; Functions ; Symmetric Groups ; Equivalence relations; cosets ; Counting the elements of a finite group ; Normal subgroups ; Homomorphisms ; Homomorphisms and normal subgroups ; Direct products and finite abelian groups ; Sylow theorems ; Rings ; subrings, ideals, and quotient rings ; Ring homomorphisms ; Polynomials ; From polynomials to fields ; Unique factorization domains ; Extension of fields ; Constructions with straightedge and compass ; Normal and separable extensions ; Galois theory ; Solvability
Includes index.
Keywords: Algebra, Abstract