Uniform bands.
A band (idempotent semigroup) \(B\) is \textit{uniform} if \(eBe\cong fBf\) for all \(e,f\in B\). The second author [\textit{F. Pastijn}, Acta Sci. Math. 42, 305-311 (1980; Zbl 0467.06005)] showed that any semilattice can be embedded in a uniform semilattice. The construction used therein is generalized to show that any band can be embedded in a uniform band that generates the same variety as the original.NEWLINENEWLINE An \textit{orthodox} semigroup is a regular semigroup whose idempotents form a band. It is well known that a band is uniform if and only if it is the band of idempotents of some bisimple orthodox semigroup. It is also shown that any orthodox semigroup is embeddable into a bisimple orthodox semigroup, whose band of idempotents generates the same variety as that of the original. Moreover, except when the original semigroup is a rectangular group, the larger semigroup can be chosen to be fundamental.
scientific article; zbMATH DE number 6349664
scientific article