Germs and semigroup representation theory

Abstract

Uniform representation of semigroups is introduced. It is proved that any uniform representation of an ample semigroup can be expressed as the direct sum of some representations obtained via homogenous representations on primitive adequate semigroups. Also, we give the structure of homogenous representations of primitive adequate semigroups. In addition, we consider indecomposable uniform representations of ample semigroups and their constructions.