# The universal $\mathcal{AIR}$- compactification of a semigroup

Document Type: Research Paper

Authors

University of Guilan

Abstract

In this paper we establish a characterization of abelian compact Hausdorff semigroups with unique idempotent and ideal retraction property. We also introduce a function algebra on a semitopological semigroup whose associated semigroup compactification is universal with
respect to these properties.

Keywords