Abstract Algebra
Explore groups and symmetry; rings and fields; extensions and actions. Concepts and connections are available independently of video coverage.
FOLLOW AN IDEA
Bijections
A bijection is both injective and surjective and has a two-sided inverse.
Explore concept graph · Explore connected videos
Different ways to understand it
No reviewed video yet. Explore the concept in a map or suggest a resource. Suggest a video
More concepts to explore
Binary operations
A binary operation combines two elements into one in a specified set.
Direct proof
A direct proof derives the conclusion from assumptions using justified logical steps.
Field extensions
A field extension contains a smaller field and can be viewed as its vector space.
Functions
A function assigns exactly one output to each input in its domain; its domain matters when comparing expressions.
Group homomorphisms
A homomorphism preserves group multiplication; its kernel measures failure of injectivity.
Knowledge connections
- Injective and surjective functions · Related · Map context
- Direct proof · Related · Map context
- Number systems · Related · Map context
- Functions · Related · Map context
- Inverse functions · Next concept · Map context
- Binary operations · Related · Map context
- Field extensions · Related · Map context
- Group homomorphisms · Next concept · Map context
Appears in these maps
Elementary Algebra and Functions
Explore numbers and expressions; equations and inequalities; functions and growth. Concepts and connections are available independently of video coverage.
Mathematical Foundations and Proofs
Explore sets and relations; logic and statements; proof and infinity. Concepts and connections are available independently of video coverage.