University of Guilan Journal of Algebra and Related Topics 2345-3931 4 2 2016 12 01 The universal $\mathcal{AIR}$- compactification of a semigroup 31 39 2000 EN A. Sahleh University of Guilan L. Najarpisheh University of Guilan Journal Article 2016 05 18 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<br />respect to these properties. Semitopological semigroup (universal) semigroup compactification distal function weakly almost periodic function ideal retraction property https://jart.guilan.ac.ir/article_2000_7d9dcf6b892e84c4d861076a1b649e06.pdf