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Lecture
Characters: Linear Algebraic Groups
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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.
Group Theory Basics: Subgroups and Homomorphisms
Introduces subgroups and homomorphisms in group theory, with examples for illustration.
Push-out: Categorical Perspective on Quotients
Explores the concept of push-out in group homomorphisms.
Categorical Perspective: Abelian Groups
Explores abelian groups from a categorical perspective, discussing the coproduct construction.
Endomorphisms: Matrix Equivalence
Explores endomorphisms, matrix equivalence, and the adjoint map as a group homomorphism.
Commutative algebraic groups
Covers the properties of commutative linear algebraic groups and their elements.
Group Fundamental: Structure and Applications
Explores the group fundamental structure and homomorphisms through examples and applications.
RSA Encryption: Main Concepts
Covers the main concepts behind RSA encryption and examples of homomorphisms between cyclic groups.
Chinese Remainder Theorem: Rings and Fields
Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.
Ring Homomorphisms and Ideals
Explores ring homomorphisms, bilateral ideals, ring features, and ideal operations.