Remarks on the paper "M. Kolibiar, On a construction of semigroups"

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 $T/\theta (T)$bya$\theta$-construction,where$\theta (T)$isthecongruenceon$T$definedby:$(a, b)\in \theta (T)$ifandonlyif$xa=xb$forall$x\in T$. Unfortunately, the paper contains some incorrect part. In our present paper we give a revision of the paper.