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Full Description
ALGEBRA - all the previous three editions are highly successful textbooks for the undergraduate and postgraduate students. It covers Groups, Rings, Modules and Fields, exhibits interplay of both Group and Field theory by means of Galois theory and shows insolvability of a quantic, in general, by radicals.
Excerpt from Review in the Zentralblatt Math:
"...authors ... have set high value on developing standard basics in very lucid, reasonably complete, throughout rigorous and efficiently structured a manner, without striving for an overloaded volume of encyclopedic character. No doubt, it is exactly this outstanding particularly attractive, valuable and popular. There is an abundance of highly interesting and instructive examples accompanying the entire text. Each single section comes with a very large set of related exercises. In fact, the great variety of skillfully selected exercises must be seen as another feature of this outstanding textbook. The exposition of the material of the main text is of utmost clarity and comprehensiveness. Altogether, this outstanding algebra text is a nearly perfect source for a course on the subject or for individual self-study, and that for students and teachers likewise."
NEW TO THE FOURTH EDITION:
• A section on Group Actions
• New Examples and Exercises have been added
• Solutions to a large number of exercises have been included.
Contents
Preface / Notations / Preliminaries: Sets and Mappings / Equivalence Relation / The Integers / The Axiom of Choice / Countable and Uncountable Sets / Groups: Definitions and Examples / Subgroups / Cosets and Normal Subgroups / Homomorphisms / Normalizer, Centralizer and Class Equation / Symmetric Groups / Direct Products / Automorphisms / Group Actions / Sylow's Theorems / Applications of Sylow's Theorems / Series of Groups / Finite Abelian Groups / Groups of Small Order / Rings: Definitions and Examples / Ideals and Isomorphism Theorems / Direct Product of Rings / Rings of Polynomials / Fields of Fractions / Prime Ideals and Maximal Ideals / Factorization in Integral Domains / Noetherian Rings / Modules: Definitions and Examples / Module Homomorphisms and Quotient Modules / Direct Sums and Exact Sequences / Free Modules / Free Modules over PIDs / Finitely Generated Modules over PIDs / Projective and Injective Modules / Semisimple Modules / Fields: Field Extensions / Splitting Fields / Algebraically Closed Fields / Normal Extensions / Separable Extensions / Galois Theory / Galois Group of a Polynomial / Radical Extensions / Constructibility / Appendix / Bibliography / Index.
