Concept
Zero divisor
A non-zero element that multiplies with another non-zero element to give zero, which no field can contain.
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
Numbers that wrap
A clock does arithmetic. It has finitely many numbers, addition never leaves it, and multiplication behaves entirely differently depending on one property of the size of the dial.
The field with four elements
The integers modulo four are not a field: two times two is zero and two has no reciprocal. There is nevertheless a field with four elements, and building it means giving up on counting as the way to make arithmetic finite.
Named alongside it
The objects these essays reach for when they reach for this one.
Modular arithmeticCharacteristicClosureCompositeCounterexampleCyclic groupFermats little theoremFinite fieldGreatest common divisorIrreducible polynomialModulusOrbit