On the expansion map of lattices
Abstract 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.
Authors
- M. Al Tahan (ORCID: https://orcid.org/0000-0002-4243-7935)
- Tapatee Sahoo (ORCID: https://orcid.org/0000-0003-0115-6675)
- Syam Prasad Kuncham (ORCID: https://orcid.org/0000-0002-1241-6885)
- Harikrishnan Panackal
- Pallavi Panjarike (ORCID: https://orcid.org/0000-0002-2407-8828)
- Aishwarya Neralakatte Nayak
Institutions
- Abu Dhabi University (AE)
- Manipal Academy of Higher Education (IN)
Publication Details
- Journal
- Afrika Matematika
- Published
- 2025-01-29
- DOI
- https://doi.org/10.1007/s13370-025-01267-z
- Primary Topic
- Rings, Modules, and Algebras
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Department of Science and Technology, Ministry of Science and Technology, India
- Science and Engineering Research Board