  Firstly, we compare the bounded derived categories with respect to the
pure-exact and the usual exact structures, and describe bounded derived
category by pure-projective modules, under a fairly strong assumption on the
ring. Then, we study Verdier quotient of bounded pure derived category modulo
the bounded homotopy category of pure-projective modules, which is called a
pure singularity category since we show that it reflects the finiteness of
pure-global dimension of rings. Moreover, invariance of pure singularity in a
recollement of bounded pure derived categories is studied.
