The projective line over a division ring results in a single auxiliary point . Examples include the real projective line, the complex projective line, and the projective line over quaternions. These examples of topological rings have the projective line as their one-point compactifications. The case of the complex number field C has the Möbius group as its homography group. For the rational numbers Q, homogeneity of coordinates means that every element of P(Q) may be represented by an element of P(Z). Similarly, a homography of P(Q) corresponds to an element of the modular group, the automorphisms of P(Z).