Quasi covering dimension of finite distributive lattices
Xiaolin Huang, Kaiyun Wang · Filomat · 2025
In this paper, we study the quasi covering dimension dimq of finite distributive lattices. By the join-irreducible elements, we characterize the dense elements of a finite lattice. Based on the notion of the widths of posets, we prove that for every finite distributive lattice \dim_q(L) = \max\{ \operatorname{width}(\uparrow a \cap J(L)) \mid a \in \operatorname{Min}(J(L)) \} - 1, where \operatorname{Min}(J(L)) is the set of all minimal elements of join-irreducible elements of L. Finally, we study the quasi covering dimension of the linear sum and rectangular product of two finite distributive lattices.