Right Clifford restriction semigroups

Abstract

Right C-restriction semigroups are the common generalizations of right C-rpp semigroups and right C-lpp semigroups. The structure of such a semigroup is established in terms of the [Formula: see text]-product of a right regular band and a C-restriction semigroup. As its applications, we give the structures of right C-rpp semigroups and right C-lpp semigroups. Also, we give the dual wreath product structure of right C-restriction semigroups. These results extend the related results in (Semigroup Forum 68 (2004) 280–292) and (Algebra Colloquium 14 (2007) 285–294).