Groups & Rings: Morphisms, Kernels, and Injectivity

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Related lectures (31)

Group Homomorphisms: Kernels, Images, and Normal Subgroups Log in to Mediaspace to watch this video

Explores group homomorphisms, kernels, images, and normal subgroups, using the dihedral group D_n as an example.

Categorical Perspective: Group Quotients Log in to Mediaspace to watch this video

Explores the categorical sense of constructing a group quotient by a normal subgroup, showing it as a specific example of a more general construction.

Homomorphisms and Isomorphisms Log in to Mediaspace to watch this video

Explores homomorphisms, isomorphisms, group properties, and their applications through examples and exercises.

Applications of Lagrange's Theorem Log in to Mediaspace to watch this video

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

Abelian Groups: Free Abelian Groups Log in to Mediaspace to watch this video

Explores free abelian groups, homomorphisms, and exact sequences in group theory.

Universal Property of Groups Log in to Mediaspace to watch this video

Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.

Group Theory: Quotients of Group Log in to Mediaspace to watch this video

Covers normal subgroups, quotient groups, homomorphisms, and the categorical viewpoint in group theory.

Group Theory Fundamentals Log in to Mediaspace to watch this video

Introduces group theory basics and group action concepts with associated subsets.

Lagrange's Theorem: Applications and Homomorphisms Log in to Mediaspace to watch this video

Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.

Isomorphism Theorems: Quotients of Group Log in to Mediaspace to watch this video

Explores the isomorphism theorems for quotient groups and the concept of surjective homomorphisms.

Morphism of Groups Log in to Mediaspace to watch this video

Covers the concept of morphism of groups, actions on sets, and automorphisms.

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