TY - JOUR
T1 - On the expansion map of lattices
AU - Panjarike, Pallavi
AU - Kuncham, Syam Prasad
AU - Nayak, Aishwarya Neralakatte
AU - Al-Tahan, Madeleine
AU - Sahoo, Tapatee
AU - Panackal, Harikrishnan
N1 - Publisher Copyright:
© The Author(s) 2025.
PY - 2025/3
Y1 - 2025/3
N2 - 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.
AB - 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.
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U2 - 10.1007/s13370-025-01267-z
DO - 10.1007/s13370-025-01267-z
M3 - Article
AN - SCOPUS:85217453440
SN - 1012-9405
VL - 36
JO - Afrika Matematika
JF - Afrika Matematika
IS - 1
M1 - 44
ER -