Algebraic Extensions of Fields - download pdf or read online

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 arrange graduate scholars for the additional learn of fields, specifically algebraic quantity conception and sophistication box conception. It presumes a few familiarity with topology and an excellent heritage in summary algebra.
Chapter 1 comprises the elemental effects relating algebraic extensions. as well as separable and inseparable extensions and general extensions, there are sections on finite fields, algebraically closed fields, primitive components, and norms and lines. bankruptcy 2 is dedicated to Galois thought. along with the basic theorum of Galois conception and a few examples, it includes discussions of cyclic extensions, Abelian extensions (Kummer theory), and the recommendations of polynomial equations via radicals. bankruptcy 2 concludes with 3 sections dedicated to the learn of endless algebraic extensions.
The examine of valuation conception, together with an intensive dialogue of prolongations of valuations, starts with bankruptcy three. bankruptcy four is anxious with extensions of valuated box, and specifically, with extensions of whole valuated fields. bankruptcy five incorporates 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 incorporates a dialogue of extensions of such fields.
A exact characteristic of this ebook is its greater than two hundred routines - lots of which comprise new principles and robust purposes - allowing scholars to determine theoretical effects studied within the textual content amplified via integration with those concrete exercises.

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Algebraic Extensions of Fields by Paul J. McCarthy

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