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Graduate Courses
21-715 Commutative Algebra
12 units
Commutative ideal theory: localization, prime spectrum, integral dependence, free and projective modules, primary decomposition, Krull dimension, fractional ideals, Dedekind domains, Hilbert finite basis theorem, Hilbert Nullstellensatz, affine algebraic varieties, coordinatization. Valuation theory: normed fields, completion, p-adic fields, Ostrowski's theorem, valuations, discrete valuations, Hensel's lemma, local fields.
Prerequisite: 21-610.
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