Characterizations of Standard Elements in Posets

Abstract

These results suggest that photocopier toner dust may be a previously unrecognized antigen in the pathophysiology of some patients diagnosed with sarcoidosis.

Genome-Wide Association Study of African and European Americans Implicates Multiple Shared and Ethnic Specific Loci in Sarcoidosis Susceptibility

“…While the etiology of this disease remains elusive, the pathophysiology likely involves a dysregulated immune response to environmental agents in a genetically susceptible host. Several environmental exposures have been associated with sarcoidosis including mold, inorganic particles, and insecticides [4], [5], [6]. A significant genetic component to sarcoidosis susceptibility is supported by a 2.5 fold elevated disease risk in siblings and parents of cases [7] as well as potential disease susceptibility loci identified from both linkage and association studies [8], [9], [10], [11], [12].…”

A note on neutral elements in posets

“…An element of a poset with 0 is called ∇-standard if ( , ) ℓ = {0} for ∈ implies ∇ ; see W a p h a r e and J o s h i [10].…”

A new view of relationship between atomic posets and complete (algebraic) lattices

“…A finite poset can be visualized through its Hasse diagram (discrete graphs), which depicts the ordering relation [35]. This area of order theory was investigated in a series of papers by Erné [16,18] and independently by Chajda, Halas, Larmerová, Rachånek, Niederle [8,[26][27][28][29]31], and later by Joshi, Kharat, Mokbel, Mundlik, Waphare [33,45,46] and many others. In [19], they are mainly interested in ideal-theoretic properties and various degrees of (finite or infinite) distributivity in atomic posets.…”