On the refined decomposition structure of left \(C\)-rpp semigroups (Q1586846)

``rpp-semigroups'' were introduced axiomatically by J. Fountain. A slight strengthening of the axioms yields the ``\(C\)-rpp semigroups'', which may be characterized as the strong semilattices of left cancellative monoids. A further slight strengthening leads to the ``left \(C\)-rpp semigroups'' of the current paper. The author investigates the decomposition of such semigroups into ``refined'' strong semilattices of direct products of left cancellative monoids and left zero bands.