On Ordered Quasi-Gamma-Ideals of Regular Ordered Gamma-Semigroups | Zendy

Mohammad Yahya Abbasi | Zendy; Abul Basar | Zendy

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On Ordered Quasi-Gamma-Ideals of Regular Ordered Gamma-Semigroups

Author(s) -

Mohammad Yahya Abbasi,

Abul Basar

Publication year - 2013

Publication title -

algebra

Language(s) - English

Resource type - Journals

eISSN - 2314-4114

pISSN - 2314-4106

DOI - 10.1155/2013/565848

Subject(s) - ideal (ethics) , mathematics , partially ordered set , minimal ideal , ordered set , semigroup , pure mathematics , combinatorics , discrete mathematics , maximal ideal , philosophy , epistemology

We introduce the notion of ordered quasi--ideals of regular ordered -semigroups and study the basic properties of ordered quasi--ideals of ordered -semigroups. We also characterize regular ordered -semigroups in terms of their ordered quasi--ideals, ordered right -ideals, and left -ideals. Finally, we have shown that (i) a partially ordered -semigroup is regular if and only if for every ordered bi--ideal , every ordered -ideal , and every ordered quasi--ideal , we have and (ii) a partially ordered -semigroup is regular if and only if for every ordered quasi--ideal , every ordered left -ideal , and every ordered right--ideal , we have that .

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