Concept
Rank of an abelian group
Related lectures (32)
A Lemma: Introduction to Homology Groups
Introduces the concept of homology groups and focuses on a lemma about free abelian groups.
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Explores the concept of free abelian groups as an important left adjoint functor.
Simple Modules: Schur's Lemma
Covers simple modules, endomorphisms, and Schur's lemma in module theory.
Group Presentations: Abelian Groups
Covers exact sequences, torsion, divisibility, and operations on abelian groups.
Fault Tolerance: Stabilizer Formalism
Covers the stabilizer formalism and fault tolerance in quantum error correction.
Simplicial Homology: Structure and Complexes
Covers the structure of topological spaces with A-complexes and chain complexes.
The Topological Künneth Theorem
Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.
Conformal Transformations: Theory and Applications
Explores the theory and applications of conformal transformations, covering special conformal transformations and isomorphic transformations.
Categorical Perspective: Abelian Groups
Explores abelian groups from a categorical perspective, discussing the coproduct construction.
Algebra: Chain Complexes
Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.