Algebras and Field Extensions

Related lectures (31)

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Covers the construction and universal properties of pushouts in group theory.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Covers the Galois correspondence, relating subgroups to intermediate fields.

Covers the density theorem in representation theory, focusing on endomorphisms of simple finite-dimensional modules.

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

Explores Cayley tables, group operations, homomorphisms, Lie groups, and differentiable groups.

Covers the properties of finite dimensional algebras and non-semisimple representations.

Explores congruence relations in rings, principal ideals, ring homomorphisms, and the characteristic of rings.

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.