Projective special linear group of degree two

Definition

The special linear group of degree two over a field $k$, or more generally over a commutative unital ring $R$, is defined as the quotient of the special linear group of degree two over the same field or commutative unital ring by the subgroup of scalar matrices in that group. The group is denoted by $PSL(2,R)$ or $PS{L}_2(R)$.