Linear fractional transformation

In mathematics, the phrase linear fractional transformation usually refers to a Möbius transformation, which is a homography on the complex projective line P(C) where C is the field of complex numbers.

More generally in mathematics, C may be replaced by another ring (A, +, ×). Then a linear fractional transformation refers to a homography over P(A), the projective line over a ring. When A is a commutative ring, then the linear fractional transformation has the familiar form