Eight colors illustrate the projective line over Galois field GF(7) In mathematics, the projective line over a ring is an extension of the concept of projective line over a field. Given a ring A (with 1), the projective line P1(A) over A consists of points identified by projective coordinates. Let A× be the group of units of A; pairs (a, b) and (c, d) from A × A are related when there is a u in A×