Module Structure: Submodules and Ring Ideals

Related lectures (32)

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Covers ideals, representations, modules, and maximal ideals in associative algebras.

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

Explores chain conditions in module theory, emphasizing Noetherian modules and stabilizing sequences of submodules.

Explores the dimension theory of rings, focusing on chains of ideals and prime ideals.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

Covers rings, modules, exact sequences, and finitely generated modules in the context of Noetherian and Artinian properties.

Introduces Noetherian modules and explores simple modules and composition series.

Explores primary decomposition in rings, focusing on primary ideals and their properties.

Introduces the definition and examples of A-modules, including sub-modules and ideals.

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.