M.S. Level Material

M.S. Algebra Syllabus

Advanced Algebra

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

References

Dummit and Foote: Abstract Algebra
Hungerford: Algebra
Lang: Algebra
Rotman: Advanced Modern Algebra