Hyperfilters and Convex Subhyperlattices in a Join Hyperlattice

N. Aishwarya Nayak (), Pallavi Panjarike (), Syam Prasad Kuncham (), Tapatee Sahoo () and Harikrishnan Panackal ()
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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

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 3, 1036-1047

Abstract: 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.

Keywords: Hyperideal; Hyperfilter; Convex set; Hyperlattice; 06B75; 06D50; 06B05 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-025-00819-0

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