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 _d is established, where the integer exponents of the generating shift (X) and clock (Z) operators are associated with submodules of ^2_d. Under this correspondence, the set of operators commuting with a given one -- a perp-set -- represents a _d-submodule of

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... 2_d. A crucial novel feature here is that the operators are also represented by non-admissible pairs of ^2_d. This additional degree of freedom makes it possible to view any perp-set as a set-theoretic union of the corresponding points of the associated projective line.