Regular semigroups with (REP) and (REP)\(^{\text{op}}\) are not necessarily amalgamation bases (Q5939560)

A semigroup \(S\) is called an amalgamation base in the class of all semigroups if for any semigroups \(T_i\) (\(i\in I\)) containing \(S\) as a subsemigroup the semigroup amalgam \([T_i;S]\) is embeddable in a semigroup. The paper is a continuation of a series of papers by the author devoted to amalgamation bases for semigroups and the representation extension property (REP) of semigroups (due to J. M. Howie). The main result is the construction of a so called finite CN-band which has REP and its dual REP\(^{\text{op}}\) but is not a semigroup amalgamation base. This gives a negative solution to a problem proposed by the author in one of his previous papers and originally due to T. E. Hall.