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We show that a UV divergence of the propagator integral implies thedivergences 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. TheUV/IR mixing is defined as a UV divergence of the planar contribution and an IRsingularity of the non-planar contribution, the latter being due to the formerUV divergence, and the UV finiteness of the non-planar contribution. Someproperties of this general treatment are discussed. The UV finiteness of thenon-planar contribution and the renormalizability of the theory are not treatedbut commented. Applications are performed for the Moyal space, having a UV/IRmixing, and the $\kappa$-Minkowski space for which the two-point function atone-loop is finite.

On the UV/IR mixing of Lie algebra-type noncommutatitive $\phi^4$-theories