Factorisations in transformation semigroups

In this thesis, the fundamental semilattice of semigroups ( ), which is the special case of semilattices of semigroups ( ) and a generalization of strong semilattices of semigroups ( ) is introduced. In addition, a quasi-strong semilattice of semigroups is introduced and given a prof about a quasi-strong semilattice with number simplification has strong semilattice property. Along with these, the concept of set-valued mapping from has been examined, regular semilattice of semigroups ( ) and refined semilattice of semigroups ( ) are introduced. It has been observed that these half lattices are integrated and a generalization of the full lattices of properly designed full classes.