O-Modularity and O-Distributivity in Semilattices

Authors

  • S. N. Begum
  • M. A. Hossain
  • A. S. A. Noor

Keywords:

Ordered set, convex subordered set, semilattice, o-distributive semilattice, distributive semilattice.

Abstract

In this paper we prove that every convex subordered set of an ordered set can be written as an intersection of a down-set and an up-set. We characterize o-modular and odistributive semilattices in terms of ideals of the semilattices. The notion of o-modular, odistributive and o-standard elements has been developed. We characterize the relation among the elements.

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How to Cite

Begum, S. N., Hossain, M. A., & Noor, A. S. A. (2015). O-Modularity and O-Distributivity in Semilattices. Science & Technology Asia, 15(4), 41–48. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/41265