On Takizawa's construction for E-unitary \({\mathcal R}\)-unipotent semigroups (Q1064412)

Instead of the PL-semigroups of \textit{K. Takizawa} [Bull. Tokyo Gakugei Univ., IV. Ser., Math. Nat. Sci. 30, 21-33 (1978; Zbl 0417.20052)] used for describing E-unitary \({\mathcal R}\)-unipotent semigroups, the same goal can be achieved by a (seemingly) more general construction obtained by omitting one of the conditions in Takizawa's definition. As a matter of fact, this construction is equivalent to Takizawa's one, but yields a somewhat simpler description.