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.

We obtain the class N A of noncommutative cylindric algebras from the class CA of cylindric algebras by weakening the axiom C 4 of commuta-tivity of cylindrifications (to C * 4 , see below, and we obtain N CA from CA by omitting C 4 completely). Some motivation for studying noncommutative cylindric algebras: Noncommutative cylindric algebras (N A's) have the same " substi-tutional structure " a...