Epsilonization: Algebra Homomorphisms and Derivation Numbers

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Group Theory - Part 2

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

Groups: Definitions, Properties, and Homomorphisms

Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.

Algebra of Matrices: Properties and Fields

Covers the properties of the algebra of matrices and related concepts.

Push-out: Categorical Perspective on Quotients

Explores the concept of push-out in group homomorphisms.

Chinese Remainder Theorem: Rings and Fields

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

Amalgams: Group Pushouts

Covers the concept of amalgams, defining pushouts and quotient groups in group theory.

First Isomorphism Theorem

Covers the first isomorphism theorem in group theory and its applications.

Group Actions on Sets

Explores group actions on sets through homomorphisms and Cartesian products, illustrating their properties and equivalent definitions.

Homomorphisms: Birational Maps and Affine Varieties

Covers homomorphisms between affine varieties, birational maps, regular groups, and connectedness.

Lie Algebras: Introduction and Structure

Introduces Lie algebras, vector spaces with a special bracket operation.