Regular OS-rpp semigroups. (Q2016334)

A semigroup \(S\) is right principally projective (rpp), if for any \(a\in S\) the \(S^1\)-system \(aS^1\) is projective; an rpp semigroup is strongly rpp iff for any \(a\in S\) exists a unique idempotent \(a^\circ\) such that \(a\mathcal L^*a^\circ\) and \(a^\circ a=a\). On a strongly rpp semigroup are defined relations \(a\overline{\mathcal R}b\) iff \(a^\circ\mathcal Rb^\circ\), \(\overline{\mathcal H}=\mathcal L^*\cap\overline{\mathcal R}\) and a semigroup is called super rpp if \(\overline{\mathcal R}\) is a left congruence; a super rpp semigroup whose idempotents constitute a band is called OS-rpp semigroup. In the paper are presented several characterizations of OS-rpp semigroups whose band of idempotents is regular.