A characterization of free generating sets in MV-algebras

Abstract.

MV-algebras are a generalization of Boolean algebras. As is well known, a free generating set $\{b_i \mid i \in X\}$ for a Boolean algebra is characterized by the following simple algebraic condition: whenever A and B are finite disjoint subsets of X then $\bigwedge_{b_i\in A}\,b_i\,\wedge\,\,\bigwedge_{b_{j}\in B}\neg b_j\neq 0$. Our aim in this note is to give a similar characterization of free generating sets in MV-algebras.