The Five Lemma

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Related lectures (29)

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Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.

The Lemma of the Five: Abelian Groups

Presents the Lemma of the Five, a fundamental result in group theory.

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Function Properties: Injective, Surjective, Bijective

Explains injective, surjective, and bijective functions using examples and graphs.

Mapping Functions and Surjections

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Group Cohomology

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

Local Rings and Residues

Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.

Exact Sequences: Splitting Remarks

Explores split exact sequences in group theory with a focus on characterization and isomorphisms.

Schur's Lemma and Representations

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.