Projective Ring Line of a Specific Qudit

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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 is established, where the integer exponents of the generating shift (X) and clock (Z) operators are associated with submodules of ²d. Under this correspondence, the set of operators commuting with a given one -- a perp-set -- represents a -submodule of ²d. A crucial novel feature here is that the operators are also represented by non-admissible pairs of ²d. 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.