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Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.
Covers rings, modules, exact sequences, and finitely generated modules in the context of Noetherian and Artinian properties.
Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.
Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.
