  We show that a UV divergence of the propagator integral implies the
divergences of the UV/IR mixing in the two-point function at one-loop for a
$\phi^4$-theory on a generic Lie algebra-type noncommutative space-time. The
UV/IR mixing is defined as a UV divergence of the planar contribution and an IR
singularity of the non-planar contribution, the latter being due to the former
UV divergence, and the UV finiteness of the non-planar contribution. Some
properties of this general treatment are discussed. The UV finiteness of the
non-planar contribution and the renormalizability of the theory are not treated
but commented. Applications are performed for the Moyal space, having a UV/IR
mixing, and the $\kappa$-Minkowski space for which the two-point function at
one-loop is finite.
