Images of simple lattice polynomials (Q1344837)

Having in mind some open problems about isotone self-maps of lattices, the authors prove the following two theorems, which are intended as steps for approaching the solution of these problems. (1) For any bounded ordered set there is a lattice and a polynomial of that lattice whose image is isomorphic to a subset isomorphic to this bounded ordered set. (2) For any elements \(a\), \(b\) in any lattice the image of the polynomial \((x+a)\cdot b\) is an order sublattice.