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 P("A") over "A" consists of points identified by projective coordinates. Let "U" be the group of units of "A"; pairs ("a, b") and ("c, d") from are related when there is a "u" in "U" such that and . This relation is an equivalence relation. A typical equivalence class is written "U"["a, b"].