Semigroups with Central Idempotents
Karl Auinger · Birkhäuser Boston eBooks · 2000
For each monoid S that is an ideal extension of a nilpotent semigroup N by a group G we construct a group H such that S divides the direct product C x H for some cyclic aperiodic monoid C. This leads to an elementary proof and some refinements of certain join decomposition results by Almeida and Weil dealing with the pseudovariety of semigroups with central idempotents.