Rpp Semigroups

Let S be a semigroup. A congruence p on S is called a left cancellative monoid congruence if S/p is a left cancellative monoid. A rpp semigroup is called an F-rpp semigroup if there exists a left cancellative monoid congruence p on S1 such that each p-class of S contains a greatest element with respect to ≤l. F-rpp semigroups are a common generalization of F-inverse semigroups, F-regular semigroups and F-abundant semigroups. After obtaining some characterizations of F-rpp semigroups, we establish the construction of strongly F-rpp semigroups, a special case of F-rpp semigroups, in terms of SFR-systems. These extends the main result of Guo in [7].