Abstract
We define the Chow ring for a Q-factorial toric variety as the Stanley-Reisner ring for the corresponding fan modulo the linear equivalence relation. We also define the pull-back homomorphism and the push-forward homomorphism between the Chow rings in terms of the combinatorial structure of fans and a map of fans, and prove the projection formula without using algebro-geometric method. In the second part, we apply the GKZ-decomposition to the Q-factorial toric varieties and obtain some information when the corresponding fans are confined to have one-dimensional cones within a fixed set.
