Algebraic Structures: Modules and Morphisms

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Related lectures (32)

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Algebraic Structures of Morphism Spaces

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

Ideals and Representations

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

Decomposition of Group Algebras

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Module Theory: Chain Conditions

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

Simple Modules: Schur's Lemma

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

Tensor Products of Modules

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Sheaves and Modules

Covers sheaves and modules, including morphisms, sheafification, cocalization, and direct image properties.

Injective Modules: Ox-Modules and Injectives

Covers injective modules, Ox-modules, and their relevance in algebraic structures, emphasizing their importance in resolving acyclic resolutions and computing cohomology.

Rings and Modules: Lecture 1

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

Linear Algebra: Modules and Endomorphisms

Explores modules, endomorphisms, and linear applications in algebra, including A-modules and commutative rings.