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Weakly Prime Ideals in Involution po-Γ-Semigroups
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  • Journal title : Kyungpook mathematical journal
  • Volume 54, Issue 4,  2014, pp.629-638
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2014.54.4.629
 Title & Authors
Weakly Prime Ideals in Involution po-Γ-Semigroups
Abbasi, M.Y.; Basar, Abul;
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 Abstract
The concept of prime and weakly prime ideal in semigroups has been introduced by G. Szasz [4]. In this paper, we define the involution in po--semigroups, then we extend some results on prime, semiprime and weakly prime ideals to the involution po--semigroup S. Also, we characterize intra-regular involution po--semigroups. We establish that in the involution po--semigroup S such that the involution preserves the order, an ideal of S is prime if and only if it is both weakly prime and semiprime and if S is commutative, then the prime and weakly prime ideals of S coincide. Finally, we prove that if S is a po--semigroup with order preserving involution, then the ideals of S are prime if and only if S is intra-regular.
 Keywords
po--semigroup;involution;weakly prime ideal;
 Language
English
 Cited by
1.
A note on ordered bi- $$\Gamma $$ Γ -ideals in intra-regular ordered $$\Gamma $$ Γ -semigroups, Afrika Matematika, 2016  crossref(new windwow)
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