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 $θ$-construction. He asserted that every semigroup $T$ can be derived from the factor semigroup $T/θ(T)$ by a $θ$-construction, where $θ(T)$ is the congruence on $T$ defined by: $(a, b)\in θ(T)$ 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.

Version v5 differs from the published and the earlier versions in the following: some part of the proof of Theorem 2 are clarified, and some typing errors are corrected