DECISION AND SEPARABILITY PROBLEMS FOR BAUMSLAG–SOLITAR SEMIGROUPS
DAVID A. JACKSON · International Journal of Algebra and Computation · 2002
We show that the semigroups Sk,ℓhaving semigroup presentations k= bℓa> are residually finite and finitely separable. Generally, these semigroups have finite separating images which are finite groups and other finite separating images which are semigroups of order-increasing transformations on a finite partially ordered set. These semigroups thus have vastly different residual and separability properties than the Baumslag–Solitar groups which contain them.