MATH 328 Algebra III: Field and Galois Theory
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Field Extensions, Algebraic Extensions, Classical Straightedge and Compass Constructions, Splitting Fields, Algebraic Closure, Separable and Inseparable Extensions, Cyclotomic Polynomials and Extensions, Galois Theory, the Fundamental Theorem of Galois Theory, Finite Fields, Composite Extensions, Simple Extensions, Abelian Extensions over Rationals, Galois Groups of Polynomials, Solvable and Radical Extensions, Insolvability of the Quintic, Computation of Galois Groups over Rationals, Transcendental Extensions, Infinite Galois Groups, Noetherian Rings, Affine Varieties, Hilbert's Nullstellensatz, Localization, the Prime Spectrum of a Ring, Artinian Rings, Discrete Valuation Rings, and Dedekind Domains.
Credit units: 3 ECTS Credit units: 5, Prerequisite:
MATH 323 and MATH 327.
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