The Structure of Endomorphism monoids of Strong semilattices of left simple semigroups

Endomorphism monoids have long been of interest in universal algebra and also in the study of particular classes of algebraic structures. For any algebra, the set of endomorphisms is closed under composition and forms a monoid (that is, a semigroup with identity). The endomorphism monoid is an interesting structure from a given algebra. In this thesis we study the structure and properties of the endomorphism monoid of a strong semilattice of left simple semigroups. In such semigroup we consider mainly that the defining homomorphisms are constant or isomorphisms. For arbitrary defining homomorphisms the situation is in general extremely complicated, we have discussed some of the problems at the end of the thesis. First we consider conditions, under which the endomorphism monoids are regular, idempotent-closed, orthodox, left inverse, completely regular and idempotent. Later, as corollaries we obtain results for strong semilattices of groups which are known under the name of Clifford semigroups and we also consider strong semilattices of left or right groups as well. Both are special cases of the strong semilattices of left simple semigroups.