On a class of t-Archimedean semigroups (Q1121999)

A semigroup S is called t-archimedean iff \(\forall a,b\in S\) \(\exists u,v,x,y\in S^ 1\), \(\exists i\in {\mathbb{N}}\) such that \(ax=b^ i\), \(ya=b^ i\), \(bu=a^ i\), \(vb=a^ i\). Let G be the maximal subgroup of S, \({\mathcal K}\) the class of all t-archimedean semigroups having an idempotent e as the only nontrivial nilsubsemigroup. If S belongs to \({\mathcal K}\) and G is finite, then every \(x\in S\setminus G\) is a product of a finite number of indecomposable elements. The set U of indecomposable elements is the union of sets \(U_ g=\{u\in U\); \(ue=g\}\), \(g\in G\) and S can be described in terms of G and words over U.