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Doctorate Algebra Syllabus
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M.S. Algebra Syllabus
Groups
- Series of groups (Jordan-Holder Theorem), solvable and nilpotent groups
- Representation theory (Maschke's Theorem)
Rings
- Modules
- Division rings (Wedderburn's Theorem)
- Noetherian rings (Hilbert Basis Theorem, power series rings), localization
- Semi-simple rings (Density Theorem)
- Gröbner Bases
- Affine algebraic varieties
Fields
- Separable, inseparable and purely inseparable extensions, normal extensions
- Transcendental extensions (transcendence bases)
- Galois theory
Dummit and Foote: Abstract Algebra
Hungerford: Algebra
Lang: Algebra
Rotman: Advanced Modern Algebra
© 2000-2008, University of Miami Department of Mathematics.
Questions or Comments to: webmaster@math.miami.edu
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