Pre-compatible almost endomorphisms and semigroups whose cube is a band.
The main result of the paper (Theorem~3) is a construction for an arbitrary semigroup whose cube is a given band \(L\). The (moderately bulky) construction is formulated in terms of certain families of mappings on \(L\). As an application the author presents a diagram of a 33-element lattice and claims that this is the subvariety lattice of the variety defined by the identity \(xyz=xywyz\) (Corollary~6). The proofs of Theorem~3 and Corollary~6 are only outlined. Reviewer's remarks: 1. The diagram is incomplete: it omits several lines between points that represent comparable varieties. 2. The author attributes the description of the lattice of varieties of semigroups whose square is a rectangular band to \textit{M. Petrich} [Semigroup Forum 7, 104-152 (1974; Zbl 0282.20048)] while it was first found by \textit{I. I. Mel'nik} [Izv. Vyssh. Uchebn. Zaved., Mat. 1971, No. 12(115), 103-108 (1971; Zbl 0241.20047)].
scientific article; zbMATH DE number 2078226