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

Andreas Distler; Victor Maltcev; Abdullahi Umar

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

Group Theory 2013-10-09 v2

Authors: Andreas Distler , Victor Maltcev , Abdullahi Umar

Abstract

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

Keywords

stability theory

Cite

@article{arxiv.1302.0985,
  title  = {$\mathcal{J}^{\ast}=\mathcal{D}^{\ast}$ need not hold in finite semigroups},
  author = {Andreas Distler and Victor Maltcev and Abdullahi Umar},
  journal= {arXiv preprint arXiv:1302.0985},
  year   = {2013}
}

Comments

This 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

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

Abstract

Keywords

Cite

Comments

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