We construct Nijenhuis operators from particular bialgebras called dendriform-Nijenhuis bialgebras. It turns out that such Nijenhuis operators commute with TD-operators, a kind of Baxter-Rota operators, and are therefore closely related to dendriform trialgebras. This allows the construction of associative algebras, called dendriform-Nijenhuis algebras, made out of nine operations and presentin...

In [4] we characterize the class of countable completey representable relation and cylindric algebras via special neat embeddings. In this note we provide a counterexample showing that the condition of countability cannot be omitted.