Quasi covering dimension of finite distributive lattices

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 _q(L) = max\{ width(↑ a ∩ J(L)) a ∈ Min(J(L)) \} - 1, where 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.