MAXIMAL PROPERTIES OF SOME SUBSEMIBANDS OF ORDER-PRESERVING FULL TRANSFORMATIONS
Ping Zhao, Mei Yang · Bulletin of the Korean Mathematical Society · 2013
Let [ $n$ ] = {1, 2, ${\ldots}$ , $n$ } be ordered in the standard way. The order-preserving full transformation semigroup ${\mathcal{O}}_n$ is the set of all order-preserving singular full transformations on [ $n$ ] under composition. For this semigroup we describe maximal subsemibands, maximal regular subsemibands, locally maximal regular subsemibands, and completely obtain their classification.