cyclotomic fields
Unity root extensions
Cyclotomic fields are number fields generated by roots of unity—complex numbers that equal 1 when raised to some power.
The simplest example comes from adjoining a primitive nth root of unity to the rational numbers.
These fields have elegant arithmetic properties and play a central role in algebraic number theory, particularly in studying Fermat's Last Theorem and class field theory.
Galois
Verb form variation system
arithmetic
Secondary consequence of action
- splittingDividing into parts
- inertInactive, physically or chemically
- Fermat's Last TheoremNo integer cubes sum to cubes
- indexAlphabetical guide to contents
algebraic
Cannot be simplified further
- degreeUnit of measurement
- coefficientsNumerical multipliers in expressions
- basisUnderlying support or principle
- discriminantFormula determining root nature
roots
Exponent's inverse operation
- complex planeCoordinate system for imaginaries
- Euler's formulae^(ix) relates to trigonometry
- cosineRatio in triangle math
- sineOpposite over hypotenuse
conjugation
Verb form variation system
ramification
Secondary consequence of action
- splittingDividing into parts
- inertInactive, physically or chemically
- Fermat's Last TheoremNo integer cubes sum to cubes
irreducible
Cannot be simplified further
- degreeUnit of measurement
- coefficientsNumerical multipliers in expressions
- basisUnderlying support or principle
Bernoulli numbers
Rational sequence in analysis
nth root
Exponent's inverse operation
- complex planeCoordinate system for imaginaries
- Euler's formulae^(ix) relates to trigonometry
- cosineRatio in triangle math
sine · argument · period · regular polygon
- number theoryprime numbers, prime, composite, integer, divisor
- fieldsbiology, chemistry, physics, mathematics, engineering