Tensor products of Leibniz bimodules and Grothendieck rings -- an addendum

We continue our investigation of certain associativity properties (namely, alternativity, power-associativity, or being a Jordan ring) of the non-associative multiplication defined on the Grothendieck group of the category of finite-dimensional Leibniz bimodules which we started in \cite{FW}. Namely, we prove that for every finite-dimensional non-zero Leibniz algebra over an arbitrary field this Grothendieck ring is not power-associative. As a consequence, the Grothendieck ring is also neither alternative nor a Jordan ring. This corrects and generalizes some of our results in the last section of \cite{FW}.