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<p>It is well known that the closure operator on a lattice is an extensive, isotone, and idempotent map. In this paper, we extend this concept by introducing the notion of an expansion map on lattices, which serves as a generalization of closure operators. The focus is to explore the properties of the collection of all expansion maps on a lattice, which forms a lattice. We delve into the discussion of their covering relation and present a comprehensive characterization of the atoms and dual atoms within the lattice obtained from these expansion maps.</p>

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On the expansion map of lattices

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月29日

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  • Pallavi Panjarike,
  • Syam Prasad Kuncham,
  • Aishwarya Neralakatte Nayak,
  • Madeleine Al-Tahan,
  • Tapatee Sahoo,
  • Harikrishnan Panackal

摘要

It is well known that the closure operator on a lattice is an extensive, isotone, and idempotent map. In this paper, we extend this concept by introducing the notion of an expansion map on lattices, which serves as a generalization of closure operators. The focus is to explore the properties of the collection of all expansion maps on a lattice, which forms a lattice. We delve into the discussion of their covering relation and present a comprehensive characterization of the atoms and dual atoms within the lattice obtained from these expansion maps.