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Structure theorem for finitely generated modules over a principal ideal domain
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Related lectures (30)
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Algebraic Structures: Modules and Morphisms
Explores modules, sub-modules, and morphisms in algebraic structures.
Subrepresentations of the regular representation
Explores subrepresentations of the regular representation in group theory, emphasizing properties and isomorphism between subrepresentations.
Topology of Riemann Surfaces
Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.
Isotypic Decomposition: Finitely Generated C-Algebras
Explores isotypic decomposition in finitely generated C-algebras and its implications, including G-stable ideals and linear projections.
Endomorphisms and automorphisms of totally disconnected locally compact groups II
Explores flat groups of automorphisms and their properties, including minimization functions and invariance under specific conditions.
Bar Construction: Homology Groups and Classifying Space
Covers the bar construction method, homology groups, classifying space, and the Hopf formula.
Finite Fields: Construction and Properties
Explores the construction and properties of finite fields, including irreducible polynomials and the Chinese Remainder Theorem.
Chinese Remainder Theorem: Euclidean Domains
Explores the Chinese Remainder Theorem for Euclidean domains and the properties of commutative rings and fields.
Congruence Relations in Rings
Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.
Group Cohomology
Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.