Subsemigroups Of A Bicyclic Semigroup

Special subsemigroups of a bicyclic semigroup are studied and an equivalent condition that its subsemigroup F_l is a full inverse subsemigroup is obtained.It is proved that the normal subsemigroup can be expressed by B_d.Meanwhile,it is showed that the set B comprised of the normal subsemigroup B_d on a bicyclic semigroup is a distributive lattice and the set T made up of congruences ρ_d on a bicyclic semigroup is a lattice,which is isomorphic to the lattice B.