Heights of posets associated with Green's relations on semigroups

Matthew Brookes, Craig Miller

Given a semigroup $S$, for each Green's relation $\mathcal{K}\in \{\mathcal{L},\mathcal{R},\mathcal{J},\mathcal{H}\}$ on $S,$ the $\mathcal{K}$-height of $S,$ denoted by $H_{\mathca…