Residual finiteness of a class of semigroups presented by a single relation
A semigroup \(S\) is said to be residually finite if for every pair of elements \(x\), \(y\) in \(S\), \(x \neq y\), there exists a congruence \(\rho\) on \(S\) such that \(S/\rho\) is finite and \([x]_ \rho \neq [y]_ \rho\). In the paper it is proved that the semigroups \(S_ k\) presented by \(\langle a,b;\;b(ab)^ kb = ab\rangle\) (\(k \geq 0\)) are all residually finite. Connections between the residual finiteness of a semigroup \(S\) and decidability of the word problem for presentations of \(S\) are discussed.
scientific article; zbMATH DE number 549061