Algebras And Representations Of Right Ample Semigroups

In this thesis, we study algebras and matrix representations of right ample semigroups. This thesis is divided into three chapters.In Chapter 1, after listing some related concepts and some known re-sults, we obtain some properties of right ample semigroups.In Chapter 2, we investigate algebras of right ample semigroups. Some properties of pseudo-RA semigroups are obtained. It is proved that any algebra of pseudo-RA semigroups with finite idempotents has a generalized matrix representation. As an application, we have proved that any algebra of finite right ample monoids has a generalized upper triangular matrix rep-resentation. Finally, we determine when algebras of pseudo-RA semigroups with finite idempotents are left self-injective. This partially answer an open problem of Okninski on left (right) self-injective semigroup algebras.In Chapter 3, we research matrix representations of right ample semi-groups. We originally introduce the notion of (left; right) uniform repre-sentation. Some properties of left uniform representations of right ample semigroups are obtained. In particular, the construction of left uniform representations of right ample semigroups are established.