Lectures related to Length of a module

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Explores the intersection multiplicity of curves and the absence of common tangent lines.

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

Explores Bézout's theorem and Cayley-Bacharach, discussing intersection multiplicities and linear combinations in projective geometry.

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

Introduces Noetherian modules and explores simple modules and composition series.

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