Clifford semilattice decompositions of stratified normal bands of monoids (Q1573082)

A normal band is an idempotent semigroup satisfying the identity \(xyzx=xzyx\). Suppose \(S\) is a semigroup that is a normal band \(E\) of monoids \(\{S_i\}_{i\in E}\). Then \(S\) is called stratified if the identity elements of the monoids \(S_i\) form a right-zero subsemigroup of \(S\). The author proves that if \(S\) is a stratified normal band of monoids, then \(S\) is isomorphic to a Clifford semilattice of Rees matrix semigroups over some of these monoids.