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.
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[Kulkarni Venkatesh, Shabbir Ahmed and Syed Waseem Raja (2014); Ideals Purity on Smooth Semigroups Int. J. of Adv. Res. 2 (2). 0] (ISSN 2320-5407). www.journalijar.com
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