Some new closures on orders

Mathematica Slovaca

Gábor Czédli¹ 

关键词: lattice;    order;    Galois connection;    Galois closure;    concept lattice;    formal concept analysis;   

DOI  :  10.2478/s12175-011-0053-y

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

For each of the relations “less than or equal to”, “less than”, “covered by”, and “covered by or equal to”, we characterize finite orders (also called posets) with the property that the pair of Galois closure operators induced by the relation in question coincides with the pair of closure operators introduced and applied in our previous paper in 2007. We also consider the “less than or equal to” relation between the set of join-irreducible elements and the set of meet-irreducible elements, and we show that the above-mentioned pairs of closure operators coincide for finite modular lattices.

【 授权许可】

Unknown