Module over a Ring

Related lectures (32)

Introduces ring theory, covering definitions, examples, and subrings criteria.

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

Covers free resolution of modules and projective modules in module theory.

Covers the isotopic decomposition of modules into simple components and their properties.

Covers the properties of finite dimensional algebras and non-semisimple representations.

Explains submodules, generated modules, and ring ideals in module structure.

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Introduces sub-rings and morphisms in ring theory, emphasizing stability by multiplication.

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

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Explores the long exact sequence of Ext-modules and their computations in homological algebra.

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

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