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The principal objective of this book is to make the general theory of field extensions accessible to any reader with a modest background in groups, rings and vector spaces. Galois theory is generally regarded as one of the central and most beautiful parts of algebra and its creation marked the culmination of investigations by generations of mathematicians on one of the oldest problems in algebra, the solvability of polynomial equations by radicals.
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Inside This Book
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First Sentence:
A basic relationship between the field Q and its subdomain Z with which the reader is already familiar is that every element of Q can be expressed as a fraction with numerator and denominator in Z. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
proper finite extension, pure inseparability, field monomorphisms, algebraically closed extension field, simple transcendental extension, separating transcendence base, preceding corollary shows, linear disjointness, verify the following assertions, factorial domain, preceding proposition shows, linear base, finite transcendence degree, purely transcendental extension, prime subfield, purely inseparable extension, radical sequence, transcendence bases, linear degree, only subfield, left transversal, valuation domain, splitting field, intermediate fields, separable polynomial Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, F-subspace of Map, Examples Let, Factorization of Polynomials, Derivations of Algebraic Function Fields, Proof Assume, Proof First, Therefore Gal New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
A basic relationship between the field Q and its subdomain Z with which the reader is already familiar is that every element of Q can be expressed as a fraction with numerator and denominator in Z. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
proper finite extension, pure inseparability, field monomorphisms, algebraically closed extension field, simple transcendental extension, separating transcendence base, preceding corollary shows, linear disjointness, verify the following assertions, factorial domain, preceding proposition shows, linear base, finite transcendence degree, purely transcendental extension, prime subfield, purely inseparable extension, radical sequence, transcendence bases, linear degree, only subfield, left transversal, valuation domain, splitting field, intermediate fields, separable polynomial Key Phrases - Capitalized Phrases (CAPs): (learn more)
Proof Let, F-subspace of Map, Examples Let, Factorization of Polynomials, Derivations of Algebraic Function Fields, Proof Assume, Proof First, Therefore Gal New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 47
books:
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22
books
cite this book:
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- Graph Theory by W. T. Tutte in Front Matter (1), Front Matter (2), and Front Matter (3)
- Finite Fields (Encyclopedia of Mathematics and its Applications) by Rudolf Lidl in Front Matter, and Back Matter
- Galois Theory: Lectures Delivered at the University of Notre Dame (Notre Dame Mathematical Lectures, Number 2) by Emil Artin in Back Matter (1), and Back Matter (2)
- Commutative Rings by Irving Kaplansky in Back Matter
- Local Fields (Graduate Texts in Mathematics) by Jean-Pierre Serre in Back Matter
See all 47 books this book cites
- Combinatorial Matrix Theory (Encyclopedia of Mathematics and its Applications) by Richard A. Brualdi in Front Matter
- Skew Fields: Theory of General Division Rings (Encyclopedia of Mathematics and its Applications) by P. M. Cohn FRS in Front Matter
- Convex Bodies: The Brunn-Minkowski Theory (Encyclopedia of Mathematics and its Applications) by Rolf Schneider in Front Matter
- Stopping Times and Directed Processes (Encyclopedia of Mathematics and its Applications) by G. A. Edgar in Front Matter
- Handbook of Categorical Algebra: Volume 2, Categories and Structures (Encyclopedia of Mathematics and its Applications) (v. 2) by Francis Borceux in Front Matter
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