Semimodular Ample Semigroups

In this thesis, we study semimodular ample semigroups. The thesis is divided into five sections.In section 2, we establish some properties of the lattice of full subsemi-groups of an ample semigroup. In section 3, several classes of distributive ample semigroup are given. In section 4, we obtain a sufficient and neces-sary condition for a weak Brandt semigroup to be semimodular(resp. mod-ular; distributive). Finally, we give the main result of this thesis which is the sufficient and necessary condition for an ample semigroup to be semimod-ular (resp. modular;distributive). In particular, it is proved that an ample semigroup is modular if and only if it is distributive.