Download e-book for kindle: Algebraic Extensions of Fields by Paul J. McCarthy

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 extra examine of fields, particularly algebraic quantity conception and sophistication box conception. It presumes a few familiarity with topology and a superior historical past in summary algebra.
Chapter 1 includes the elemental effects referring to algebraic extensions. as well as separable and inseparable extensions and basic extensions, there are sections on finite fields, algebraically closed fields, primitive parts, and norms and lines. bankruptcy 2 is dedicated to Galois idea. in addition to the elemental theorum of Galois conception and a few examples, it includes discussions of cyclic extensions, Abelian extensions (Kummer theory), and the suggestions of polynomial equations by way of radicals. bankruptcy 2 concludes with 3 sections dedicated to the examine of endless algebraic extensions.
The examine of valuation concept, together with an intensive dialogue of prolongations of valuations, starts off with bankruptcy three. bankruptcy four is worried with extensions of valuated box, and specifically, with extensions of entire valuated fields. bankruptcy five includes a evidence of the original factorization theorum for beliefs of the hoop of integers of an algebraic quantity box. The remedy is valuation-theoretic all through. The bankruptcy additionally includes a dialogue of extensions of such fields.
A specified function of this booklet is its greater than 2 hundred workouts - a lot of which include new principles and robust functions - permitting 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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