The join of the pseudovarieties of \(\mathcal R\)-trivial and \(\mathcal L\)-trivial monoids (Q1262959)

The pseudovariety described in the title was previously studied by \textit{R. König} [Rairo, Inf. Théor. 19, 233-260 (1985; Zbl 0571.20066)]. The authors answer the remaining formerly open questions about this pseudovariety. In particular, they characterize it using pseudoidentities, following the approach of \textit{J. Reiterman} [Algebra Univers. 14, 1-10 (1982; Zbl 0484.08007)]. Their first such description involves a single pseudoidentity in five variables. An alternative description is given involving a single pseudoidentity in three variables. This is shown to be minimal in the sense that no set of pseudoidentities on two variables can define the required pseudovariety.