Correction to: Pre-compatible almost endomorphisms and semigroups whose cube is a band

1 Correction to: Semigroup Forum Vol. 67 (2003) 355–372 https://doi.org/10.1007/s00233-001-0004-y

In the lattice of subvarieties of the variety ${ \mathcal {V} = [xyz=xywyz]}$ depicted in p. 370, the following inclusions are missing:

$$\begin{aligned}{}[xyz = xw]&\subset [xyz=xz], \\ [xyz = wz]&\subset [xyz=xz], \\ [xyz=xy]&\subset [xyz=xyw; x^3=x^2], \\ [xyz=yz]&\subset [xyz=wyz; x^3=x^2], \\ [xyz=x^2]&\subset [xwy=xvy; x^3=x^2], \\ \text {and} \quad [xyz=z^2]&\subset [xwy=xvy; x^3=x^2]. \end{aligned}$$

The complete diagram for the lattice is given in Fig. 1. None of the other results of the paper are affected by the missing inclusions.

Fig. 1

The lattice of subvarieties of $\mathcal {V}$