On the characterization of centered Lukasiewicz algebras

Abstract The notion of a Lukasiewicz algebra was introduced in [11]. In the following we shall attempt a characterization of the centered n -valued Lukasiewicz algebras [10]. From this, it will be derived a characterization of injective Lukasiewicz algebras. For n = 3, the results of [12] are reobtained as a particular case. In this work we shall largely use functorial means [8]. We shall denote by ∪, ∩ the composition laws of a lattice, by 0, 1 the first and the last element, respectively, and by ⊂the canonical order of the lattice.