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<p>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 <i>P</i>-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 <i>P</i>-hyperlattice or Nakano hyperlattice can be uniquely represented as the intersection of a hyperideal and a hyperfilter, and illustrate with suitable examples.</p>

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Hyperfilters and Convex Subhyperlattices in a Join Hyperlattice

  • 期刊论文

  • 发表日期：

    2025年7月8日

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  • N. Aishwarya Nayak,
  • Pallavi Panjarike,
  • Syam Prasad Kuncham,
  • Tapatee Sahoo,
  • Harikrishnan Panackal

摘要

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.