Weakly Prime Ideals in Involution po-Γ-Semigroups

• 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;

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-$\small{{\Gamma}}$-semigroups, then we extend some results on prime, semiprime and weakly prime ideals to the involution po-$\small{{\Gamma}}$-semigroup S. Also, we characterize intra-regular involution po-$\small{{\Gamma}}$-semigroups. We establish that in the involution po-$\small{{\Gamma}}$-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-$\small{{\Gamma}}$-semigroup with order preserving involution, then the ideals of S are prime if and only if S is intra-regular.
Keywords
po-$\small{{\Gamma}}$-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, 27, 7-8, 1403
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