Fernandes, Vítor H.Quinteiro, Teresa Maria de Araújo Melo2011-04-202011-04-202009-07-290092-7872http://hdl.handle.net/10362/5531Communications in AlgebraIn this paper we consider the monoid O mxn of all order-preserving full transformations on a chain with mn elements that preserve a uniform m-partition and its submonoids O+ mxn and O− mxn of all extensive transformations and of all co-extensive transformations, respectively. We give formulas for the number of elements of these monoids and determine their ranks. Moreover, we construct a bilateral semidirect product decomposition of Omxn in terms of O− mxn and O+ mxn.engorder-preserving transformationsequivalence-preserving transformationsjournal article