The right dual of left \(C\)-\(rpp\) semigroups
A semigroup \(S\) is said to be \(rpp\) if every principal right ideal \(aS^1\), regarded as a right \(S\)-system, is projective. Call an \(rpp\) semigroup \(S\) a \(C\)-\(rpp\) semigroup if its idempotents lie in the centre of \(S\). In this paper, the author defines the right \(C\)-\(rpp\) semigroups by using \((\ell)\)-Green's relations and observes that the right \(C\)-\(rpp\) semigroups are the dual of the left \(C\)-\(rpp\) semigroups [see \textit{Y. Gou}, \textit{K.-P. Shum} and \textit{P. Zhu}, Semigroup Forum 50, No. 1, 9-23 (1995; Zbl 0821.20046)]. The crucial point is that the right \(C\)-\(rpp\) semigroups and left \(C\)-\(rpp\) semigroups are not symmetric, for instance, \({\mathcal L}^{(1)}={\mathcal J}^{(1)}\) on left \(C\)-\(rpp\) semigroups but \({\mathcal L}^{(1)},{\mathcal R}^{(1)}\nsubseteq{\mathcal D}^{(1)}={\mathcal J}^{(1)}\) on right \(C\)-\(rpp\) semigroups.
scientific article; zbMATH DE number 1106392