| Glrac semigroups are common generalizations of left GC-lpp semigroups and left inverse semigroups.And,such a semigroup is a left restriction semigroup if and only if the projection set is a semilattice.So,glrac semigroup is also a gen-eralization of left restriction semigroup.Permissible subsets of a glrac semigroup are introduced in this paper.In terms of permissible subsets,we define(uniquely)factorizable glrac semigroups and(uniquely)almost factroizbale glrac semigroups.Many characterizations of(uniquely)factorizable glrac semigroups and(unique-ly)almost factorizable glrac semigroups are obtained.As their applications,we establish the structures of uniquely factorizable left GC-lpp semigroups(left in-verse semigroups,inverse semigroups,ample semigroups,left restriction semigroup,restriction semigroups)and uniquely almost factorizable left GC-lpp semigroup-s(left inverse semigroups,inverse semigroups,ample semigroups,left restriction semigroup,restriction semigroups).Our results enrich and extend the related results of almost factorizable restriction semigroups of Szendrei in(Comm.Alge-bra 41(2013),1458-1483)and Gomes and Szendrei in(Comm.Algebra 35(2007),3503-3523). |
