On the expansion map of lattices

被引：0

作者：

Panjarike, Pallavi ^{[1
]}

Kuncham, Syam Prasad ^{[1
]}

Nayak, Aishwarya Neralakatte ^{[1
]}

Al-Tahan, Madeleine ^{[2
]}

Sahoo, Tapatee ^{[3
]}

Panackal, Harikrishnan ^{[1
]}

机构：

[1] Manipal Inst Technol, Manipal Acad Higher Educ, Dept Math, Manipal, Karnataka, India

[2] Abu Dhabi Univ, Dept Math & Stat, Abu Dhabi, U Arab Emirates

[3] Manipal Acad Higher Educ, Manipal Inst Technol Bengaluru, Dept Math, Bengaluru, Karnataka, India

来源：

AFRIKA MATEMATIKA | 2025年 / 36卷 / 01期

关键词：

Closure operators; Covering relation; Expansion map; 2-ABSORBING PRIMARY IDEALS;

D O I：

10.1007/s13370-025-01267-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

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.

引用

页数：12

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