Using groups of affine transformations of linearly ordered fields a certain construction of non-commutative join hypergroups is presented based on the criterion of reproducibility of semi-hypergroups which are determined by ordered semigroups. The aim of this paper is to construct the abelization of the non-commutative join space of affine transformations of ordered fields. A construction of co...

As Jonathan Leech has pointed out, many natural examples of inverse semigroups are semilattice ordered under the natural partial order. But there are many interesting examples of semilattice ordered inverse semigroups in which the imposed partial order is not the natural one. In this talk we shall explore the structure and properties of these examples and some other questions related to semilat...