Coextensions of eventually regular biordered sets by rectangular biordered sets (Q1306937)

Let \(E,F\) be biordered sets and \(\phi\colon E\to F\) a surjective morphism [for a definition see \textit{K. Auinger} and \textit{T. E. Hall}, Commun. Algebra 24, No. 12, 3933-3968 (1996; Zbl 0857.20042)]; if for all \(\alpha\in F\), \(\alpha\phi^{-1}\) is a rectangular biordered set then \(E\) is a coextension of \(F\) by rectangular biordered sets. For any eventually regular biordered set \(F\) all such coextensions are constructed. This construction extends a classical result by \textit{J. Meakin} and \textit{K. S. S. Nambooripad} concerning regular biordered sets [Trans. Am. Math. Soc. 269, 197-224 (1982; Zbl 0493.20042)]. The construction is technically difficult. A remarkable application shows that each solid eventually regular biordered set is actually regular.