Tail and free poset algebras. - Bekkali, Mohamed; Zhani, Driss (Revista Matemática Complutense, 2004)
We characterize free poset algebras F(P) over partially ordered sets and show that they can be represented by upper semi-lattice algebras. Hence, the uniqueness, in decomposition into normal form, using symmetric difference, of non-zero elements of F(P) is established. Moreover, a characterization of upper semilattice algebras that are isomorphic to free poset algebras is given in terms of a selected set of generators of B(T).