Some notes/problem sets for an algebra course
(2011)

Notes:

• Modules: basic constructions, free modules
• Modules: finiteness conditions, the determinant trick, presentations, Smith normal form
• Modules: structure theorem for abelian groups. Field extensions: basic concepts
• Field extensions: degree of an extension
• Algebras, integral dependence
• Noether normalization, Nullstellensatz, affine varieties, morphisms (Warning: there are several typos in the proof of Noether normalization)
• Irreducibility, finite morphisms, Noether normalization (geometric form)

Problem sets:

• Problem set 1
• Problem set 2
• Problem set 3
• Problem set 4
• Problem set 5
• Problem set 6
• Problem set 7
• Problem set 8

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Last updated: 23 May, 2011