  The 4-dimensional space-time is extended to pseudo-complex coordinates.
Proposing the standard quantization rules in this extended space, the ones for
the 4-dimensional sub-space acquire, as one solution, the commutation relations
with non-commuting coordinates. This demonstrates that the algebraic extension
keeps the simple structure of Quantum Mechanics, while it also introduces an
effective quite involved structure in the 4-dimensional sub-space. The
similarities to H. S. Snyder's work, a former proposal to include the effects
of a minimal length, are exposed. The first steps to pseudo-complex Quantum
Mechanics in 1-dimension are outlined, awaiting still the interpretation of
some new emerging structures. As an example, two waves, out of phase by 90
degrees, are added which classically annihilate each other, while in the
pseudo-complex description there is a non-zero amplitude.
