Localizations of tensor products

Abstract

A homomorphism $\lambda :A\to B$ between $R$-modules is called a localization if for all $\phi \in Ho{m}_R(A,B)$ there is a unique $\psi \in Ho{m}_R(B,B)$ such that $\phi =\psi \circ \lambda$ . We investigate localizations of tensor products of torsion-free abelian groups. For example, we show that the natural multiplication map $\mu :R\otimes R\to R$ is a lo cal iza tion if and only if $R$ is an E-ring.