Math 603, Spring 2005
Faculty
: David Harbater
E-mail:
harbater@math.upenn.edu
Telephone
: (215) 898-9594; Department office: (215) 898-8178
Office: DRL 4E2A; Department office: DRL 4W1-6.
Second semester graduate algebra.
Topics include:
modules: exact sequences, algebras, tensor products, 5 lemma, snake lemma, flat modules, projective modules, modules over a PID, localization, Nakayama's Lemma, locally free modules, Ext and Tor;
commutative rings: Noetherian rings and modules, Hilbert Basis Theorem, Krull dimension, primary decomposition, integral extensions, integral closure, lying over theorem, Artin rings, Dedekind domains, discrete valuation rings, Krull's principal ideal theorem;
field theory: degree of an extension, transcendence degree, algebraic closures, separable extensions, splitting fields, normal extensions, finite fields, purely inseparable extensions, Primitive Element Theorem, perfect fields;
Galois theory: Galois extensions, fixed fields, Galois groups, Fundamental Theorem of Galois Theory, Kummer's theorem, linear independence of characters, Hilbert's Theorem 90, algebraic independence of automorphisms, Artin-Schreier theorem, normal basis theorem, geometric constructibility, solvability by radicals.
There are regular problem sets, and an exam on Thursday, April 28, 11am-1pm.
Sample exam.
Homework assignments for Math 603
Problem Set 1
Problem Set 2
Problem Set 3
Problem Set 4
Problem Set 5
Problem Set 6
Problem Set 7
Problem Set 8
Problem Set 9
Problem Set 10
Problem Set 11
General information about the graduate mathematics program
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