The finite basis problem for Kiselman monoids

In an earlier paper, the second-named author has described the identities holding in the so-called Catalan monoids. Here we extend this description to a certain family of Hecke–Kiselman monoids including the Kiselman monoids Kn. As a consequence, we conclude that the identities of Kn are nonfinitely based for every n≥4 and exhibit a finite identity basis for the identities of each of the monoids K2 and K3.