On the Monoids of Transformations that Preserve the Order and a Uniform Partition
Vítor Hugo Fernandes, Teresa M. Quinteiro · Communications in Algebra · 2011
In this article we consider the monoid 𝒪 m × n of all order-preserving full transformations on a chain with mn elements that preserve a uniform m-partition and its submonoids and of all extensive transformations and of all co-extensive transformations, respectively. We determine their ranks and construct a bilateral semidirect product decomposition of 𝒪 m × n in terms of and .