${\mathcal{J}}^{\ast }={\mathcal{D}}^{\ast }$ need not hold in finite semigroups

Andreas Distler, Victor Maltcev, Abdullahi Umar

We provide an example of minimum size of a finite semigroup with ${\mathcal{J}}^{\ast }\ne {\mathcal{D}}^{\ast }$. We introduce the notion of starred stability and prove that every starr…