Module over a Ring

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Related lectures (34)

Group Cohomology

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Algebraic Kunneth Theorem

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

Cohomology: Cross Product

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

Algebraic Structures of Morphism Spaces Log in to Mediaspace to watch this video

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

Simple Modules: Schur's Lemma Log in to Mediaspace to watch this video

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

Ideals and Representations Log in to Mediaspace to watch this video

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

Ring Theory: Morphisms and Isomorphisms Log in to Mediaspace to watch this video

Covers commutative ring morphisms, subrings, and injective ring morphisms.

Module Theory: Definitions and Examples Log in to Mediaspace to watch this video

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

Dimension Theory of Rings Log in to Mediaspace to watch this video

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

Group Algebra: Maschke's Theorem Log in to Mediaspace to watch this video

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

Linear Algebra: Modules and Endomorphisms Log in to Mediaspace to watch this video

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

Module Theory: Chain Conditions Log in to Mediaspace to watch this video

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

Algebraic Structures: Modules and Morphisms Log in to Mediaspace to watch this video

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

Dedekind Rings and Fractional Ideals Log in to Mediaspace to watch this video

Explores Dedekind rings, fractional ideals, integrally closed properties, prime ideal factorization, and the structure of fractional ideals as a commutative group.

Localization in Algebra Log in to Mediaspace to watch this video

Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.

Rings and Modules: Color Codes and Homological Algebra Log in to Mediaspace to watch this video

Covers rings and modules, emphasizing color codes and homological algebra concepts.

Sheaf Morphisms and Localization Log in to Mediaspace to watch this video

Explores F-G sheaf morphisms, sheafification, and localization in ring theory.

Homomorphisms and Projective Resolutions Log in to Mediaspace to watch this video

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

Tensor Product: Bilinear Maps Log in to Mediaspace to watch this video

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

Algebraic Geometry: Localization and Prime Ideals Log in to Mediaspace to watch this video

Explores prime ideals and localization in algebraic geometry, highlighting their significance in ring structures.

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