Abstract

MONTEIRO, Luiz F.  and  FIGALLO, Aldo V.. Free k-cyclic E-lattices over a poset. Rev.colomb.mat. [online]. 2005, vol.39, n.1, pp. 57-61. ISSN 0034-7426.

In this note we consider a new equational class of algebras called E-lattices (A, ^, V, h, 0, 1) where (A, ^, V, 0, 1) is a distributive (0,1)-lattice and h is a lattice endomorphism. We consider the subclass E_k of k-cyclic E-lattices such that h^k(x) = x, for all x, k is a positive integer. We determine the structure of the free k-cyclic E-lattice over a poset using results obtained by L. Monteiro in [9[ for the free distributive lattice over a poset.

Keywords : Distributive lattices; free algebras.