Combinatorially Factorizable Restriction Monoids

Combinatorially factorizable cryptic restriction monoids are generaliza-tions of combinatorially factorizable cryptic inverse monoids in the range of restriction semigroups.The structure of such semigroups is established in terms of the semidirect products of a Clifford restriction monoid and a com-binatorial restriction monoid.As its applications,we give the constructions of combinatorially factorizable cryptic ample monoids and of combinatorial-ly factorizable cryptic inverse monoids.Our results enrich and extend the related results of Petrich(J.Canadian Math.Soc.57(2014),621-630).