Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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ON QUASI COVERED IDEALS AND QUASI BASES OF ORDERED SEMIGROUPS

  • M. Y. Abbasi (Department of Mathematics, Jamia Millia Islamia) ;
  • Shahnawaz Ali (Department of Mathematics, Jamia Millia Islamia) ;
  • S. A. Khan (Department of Mathematics, Jamia Millia Islamia)
  • Received : 2024.03.14
  • Accepted : 2024.05.18
  • Published : 2024.09.24
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Abstract

This paper explores the concepts of quasi covered ideal, quasi base and the greatest quasi covered ideal within the context of an ordered semigroup, extending the study of algebraic structures to incorporate both the algebraic and order theoretic perspectives. An ordered semigroup provides a rich framework for investigating the interplay between algebraic and order structure. Also, we provide the conditions for the greatest ideal to be quasi covered ideal and develop the fundamental properties with implications of quasi covered ideal of an ordered semigroup. Moreover, we study the relationship between covered ideal with quasi covered ideal, greatest ideal with quasi covered ideal and the greatest quasi covered ideal with quasi base of an ordered semigroup.

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Acknowledgement

The authors extend their sincere appreciation to the reviewers for their insightful comments and constructive feedback, which greatly enhanced the quality of this paper.

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