Abstract

We generalize to theories of modules (complete or not) a result of U. Felgner stating that a complete theory of abelian groups is a Horn theory if and only if it is closed under products. To prove this we show that a reduced product of modules $\Pi_F M_i (i \in I)$ is elementarily equivalent to a direct product of ultraproducts of the modules $M_i (i \in I)$