# Localizations of tensor products

### Manfred Dugas

Baylor University, Waco, USA### Kelly Aceves

Baylor University, Waco, USA### Bradley Wagner

Baylor University, Waco, USA

## Abstract

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

## Cite this article

Manfred Dugas, Kelly Aceves, Bradley Wagner, Localizations of tensor products. Rend. Sem. Mat. Univ. Padova 131 (2014), pp. 237–258

DOI 10.4171/RSMUP/131-14