Recall that multiplication turns R into a monoid. It is not necessarily the case that every (nonzero) element has an inverse with respect to multiplication. Those elements a in R that do have an inverse are called the invertible elements of R. The inverse of a in R is denoted by a-1.
Theorem
The invertible elements of R form a multiplicative group (i.e., a group with respect to multiplication).
This group is denoted by R*.
The Euler indicator can be expressed in terms of such a group:
(n) =
|(Z/nZ)*|.