Concept

Finitely generated module

Related lectures (31)

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

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

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

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

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

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

Explores isotypic decomposition in finitely generated C-algebras and its implications, including G-stable ideals and linear projections.

Covers the concept of tensor product in the context of bilinear maps and explores the uniqueness of tensor products.

Explores modules, sub-modules, and morphisms in algebraic structures.

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

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

Explores Python modules, program hierarchy, module importing, and namespaces, including variables and scopes within functions.

Introduces Noetherian modules and explores simple modules and composition series.

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

Covers homomorphisms, projective modules, and resolutions in chain complexes.

Explores module generation, submodules, modulus, finite type modules, and morphisms.

Explores adelic number theory, emphasizing lattices, modules, linear combinations, and Z-linear properties.

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

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