Separative P.I. semigroups are embeddable into a semilattice of groups (Q1110660)

A semigroup S has a permutational property if there exists \(n\geq 2\) such that for every \(s_ 1,...,s_ n\in S\) we have \(s_ 1...s_ n=s_{\sigma (1)}...s_{\sigma (n)}\) for a non-trivial permutation \(\sigma\). It is shown that every separative semigroup which has a permutational property is embeddable into a semilattice of groups. This particularly applies to semigroups S for which the semigroup algebra K[S] over a field K satisfies a polynomial identity.