Semisimple rings, Artin-Wedderburn Theorem. Prime and radical ideals, nilradical and Jacobson radical of a ring. Hilbert’s Nullstellensatz and consequences for finitely generated algebras. Localization of rings and modules. Tensor product of modules and algebras. Flat modules, projective modules, free modules, simple modules, indecomposable modules. Noetherian rings, Hilbert Basis Theorem. Valuation rings.
The prerequisites for MAT 4141 are MAT 3141 and MAT 3143. There are no official prerequisites for MAT 5141, but it is strongly recommended that students have taken MAT 3141 and MAT 3143 or equivalent courses given at other universities. (See here for a description of these courses.)
Click the above header to download lecture notes for the course. They are a single file that will be updated as the course progresses. They should be complemented by your own class notes. I will often say more in class than is in the lecture notes.
Robert Ash, Abstract Algebra: The Basic Graduate Year.
There are two main locations for information regarding the course: