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

Abstract

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 starred stable semigroup has ${\mathcal{J}}^{\ast }={\mathcal{D}}^{\ast }$.

arXiv commentThis result, though correct, does not really introduce anything important to semigroup theory. Better not to let down by this little preprint the entropy of Maths knowledge stored at arxiv