Paul J. McCarthy's Algebraic Extensions of Fields PDF

By Paul J. McCarthy

ISBN-10: 0486666514

ISBN-13: 9780486666518

ISBN-10: 0828412847

ISBN-13: 9780828412841

"...clear, unsophisticated and direct..." — Math
This textbook is meant to organize graduate scholars for the extra learn of fields, in particular algebraic quantity conception and sophistication box concept. It presumes a few familiarity with topology and an exceptional historical past in summary algebra.
Chapter 1 comprises the fundamental effects relating algebraic extensions. as well as separable and inseparable extensions and common extensions, there are sections on finite fields, algebraically closed fields, primitive components, and norms and lines. bankruptcy 2 is dedicated to Galois conception. in addition to the basic theorum of Galois concept and a few examples, it comprises discussions of cyclic extensions, Abelian extensions (Kummer theory), and the options of polynomial equations by means of radicals. bankruptcy 2 concludes with 3 sections dedicated to the learn of countless algebraic extensions.
The learn of valuation idea, together with a radical dialogue of prolongations of valuations, starts with bankruptcy three. bankruptcy four is worried with extensions of valuated box, and particularly, with extensions of whole valuated fields. bankruptcy five features a evidence of the original factorization theorum for beliefs of the hoop of integers of an algebraic quantity box. The therapy is valuation-theoretic all through. The bankruptcy additionally features a dialogue of extensions of such fields.
A distinct characteristic of this ebook is its greater than 2 hundred routines - a lot of which comprise new rules and robust functions - permitting scholars to work out theoretical effects studied within the textual content amplified through integration with those concrete exercises.

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Algebraic Extensions of Fields by Paul J. McCarthy


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