Prime power
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
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.
Seven points, seven lines
A geometry with seven points, in which every two points lie on exactly one line and every two lines meet in exactly one point. There are no parallels, the whole thing is built out of the two-element field, and one of its lines has to be drawn as a circle.
Named alongside it
The objects these essays reach for when they reach for this one.
Finite fieldBasisCharacteristicClosureCounterexampleCounting argumentDualityFano planeIncidenceIrreducible polynomialModular arithmeticProjective plane