quotient ring
Cosets form ring
A quotient ring is a ring formed by partitioning another ring into equivalence classes using an ideal, then defining operations on those classes.
The elements are cosets of the ideal, with addition and multiplication inherited from the original ring.
Quotient rings formalize the idea of "modding out" by certain elements: The integers modulo n form a quotient ring of the integers.
construction
Standard of perfection
- congruenceState of agreement
- kernelSeed or essential core
- partitionBarrier separating spaces
- well-definedHaving clear boundaries
representatives · collapsing · identification · equivalence relation
homomorphism
Seed or essential core
- imageVisual or mental likeness
- universal propertyMorphism-based defining trait
ideal
Standard of perfection
- congruenceState of agreement
- kernelSeed or essential core
- partitionBarrier separating spaces
well-defined · representatives · collapsing · identification · equivalence relation
kernel
Seed or essential core
- imageVisual or mental likeness
- universal propertyMorphism-based defining trait
units
Standard measures of quantity
- characteristicDistinguishing quality or trait
variety
State of being diverse
- cryptographyScience of secure messaging
localization
Adapting for specific markets