On the ?del? relation in join-semilattices

Characterizations of Standard Elements in Posets

“…The concept of ∇-standard element is studied in join-semilattices by Maeda, Thakare and Wasadikar [11] as a generalization of a standard element. In fact, in [11] it is proved that every standard element is ∇-standard, and the converse is true in a sectionally semi-complemented lattice.…”

“…In fact, in [11] it is proved that every standard element is ∇-standard, and the converse is true in a sectionally semi-complemented lattice. In this section, we introduce the concept of ∇-standard element in a poset and prove that the concepts of ∇-standard element, standard element and distributive element coincide in a sectionally semicomplemented poset and hence, in particular, in an atomistic poset.…”