  A very particular connection between the commutation relations of the
elements of the generalized Pauli group of a $d$-dimensional qudit, $d$ being a
product of distinct primes, and the structure of the projective line over the
(modular) ring $\bZ_{d}$ is established, where the integer exponents of the
generating shift ($X$) and clock ($Z$) operators are associated with submodules
of $\bZ^{2}_{d}$. Under this correspondence, the set of operators commuting
with a given one -- a perp-set -- represents a $\bZ_{d}$-submodule of
$\bZ^{2}_{d}$. A crucial novel feature here is that the operators are also
represented by {\it non}-admissible pairs of $\bZ^{2}_{d}$. This additional
degree of freedom makes it possible to view any perp-set as a {\it
set-theoretic} union of the corresponding points of the associated projective
line.
