Lectures related to Torsion-free module

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

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

Covers nonuniform torsion, strain energy, torsional constants, and shear flow in structural members with practical examples.

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

Covers the concepts of torsion and divisibility in group theory.

Explores torsion and divisibility in abelian groups, including p-divisible groups and their contrast with torsion elements.

Explores divisibility and torsion in group theory, focusing on defining a functor that preserves divisibility.

Covers the Five Lemma, a fundamental result in exact sequences theory.

Explores the concept of torsion in group theory, focusing on its Hom functoriality and its role in exact sequences.

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

Covers linear representations, isomorphism, G modules, and classification of representations of C star and C plus.

Introduces torsion and divisibility concepts in abelian groups to describe their structure.

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

Introduces Noetherian modules and explores simple modules and composition series.

Explores exact sequences of abelian group homomorphisms and provides examples.

Explores the theory of finite strain and rotation in Kirchhoff rods, covering inextensible strains, finite rotations, and equilibrium.

Covers free resolution of modules and projective modules in module theory.

Covers the fundamental theorem of finitely generated modules over a PID.

Covers exact sequences, torsion, divisibility, and operations on abelian groups.