Direct sum of modules

Related lectures (31)

Explores the construction and properties of the free abelian group FAb(X) and its categorical extensions.

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

Explores the concept of direct sums in abelian groups, emphasizing the universal property and homomorphisms.

Covers the properties and theorems of Boolean algebra in logic systems.

Covers the Orbit-Stabilizer theorem, conjugacy classes, and direct products in finite groups.

Explores conjugation in groups, the direct product of groups, and the classification of finite abelian groups.

Covers direct sums of abelian groups, group actions, and vector spaces, including coproducts and homomorphisms.

Explores the Lie theorem and irreducible representations in group theory.

Covers the Jordan normal form and the decomposition of vector spaces by an endomorphism.

Covers the basis for irreducible representations and characters of direct product representations.

Covers the proof of the Classification Theorem for finite abelian groups, demonstrating the existence of a decomposition into cyclic groups.

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