Title: Non-commutative crepant resolutions for some toric singularities I,
Abstract: We give a criterion for the existence of non-commutative crepant resolutions
(NCCR's) for certain toric singularities. In particular we recover Broomhead's
result that a 3-dimensional toric Gorenstein singularity has a NCCR. Our result
also yields the existence of a NCCR for a 4-dimensional toric Gorenstein
singularity which is known to have no toric NCCR.