Ideals Purity on Smooth Semigroups

Our aim in this paper is to investigate the purity of the ideals on smooth semigroups. Smooth groups were due to Warrack B.D (2006). We prove every ideal of a semigroup S is globally idempotent iff it is complete. Clifford. A. H (1999) observed some basic necessary conditions and Szas S.B(2001) indicated an analogous notion of pure subgroup of an abelian group. Further we proved A is -pure iff , and generalized the theorem of Kuroki. N (1998) to obtain some important results which are useful in poroscopy of a finger prints.