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Hyperfilters and Convex Subhyperlattices in a Join Hyperlattice

Author

Listed:
  • N. Aishwarya Nayak

    (Manipal Institute of Technology, Manipal Academy of Higher Education)

  • Pallavi Panjarike

    (Manipal Institute of Technology, Manipal Academy of Higher Education)

  • Syam Prasad Kuncham

    (Manipal Institute of Technology, Manipal Academy of Higher Education)

  • Tapatee Sahoo

    (Manipal Institute of Technology Bengaluru, Manipal Academy of Higher Education)

  • Harikrishnan Panackal

    (Manipal Institute of Technology, Manipal Academy of Higher Education)

Abstract

In this paper, we define different types of hyperfilters in a join hyperlattice. We prove that these types of hyperfilters are equivalent in a join P-hyperlattice whereas, only type-II and type-III hyperfilters are equivalent in a Nakano hyperlattice. We define the notion of convex subhyperlattice in a join hyperlattice and discuss various properties with suitable examples. Finally, we prove that any convex subhyperlattice in a P-hyperlattice or Nakano hyperlattice can be uniquely represented as the intersection of a hyperideal and a hyperfilter, and illustrate with suitable examples.

Suggested Citation

  • N. Aishwarya Nayak & Pallavi Panjarike & Syam Prasad Kuncham & Tapatee Sahoo & Harikrishnan Panackal, 2025. "Hyperfilters and Convex Subhyperlattices in a Join Hyperlattice," Indian Journal of Pure and Applied Mathematics, Springer, vol. 56(3), pages 1036-1047, September.
    • Handle: RePEc:spr:indpam:v:56:y:2025:i:3:d:10.1007_s13226-025-00819-0
    DOI: 10.1007/s13226-025-00819-0
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