Remarks on the paper “M. Kolibiar, on a construction of semigroups”

Abstract

In his paper “On a construction of semigroups”, M. Kolibiar gives a construction for a semigroup T (beginning from a semigroup S) which is said to be derived from the semigroup S by a $\theta$-construction. He asserted that every semigroup T can be derived from the factor semigroup $T/\theta (T)$ by a $\theta$-construction, where $\theta (T)$ is the congruence on T defined by: $(a, b)\in \theta (T)$ if and only if $xa=xb$ for all $x\in T$. Unfortunately, the paper contains some incorrect part. In our present paper we give a revision of the paper.