Rendiconti del Seminario Matematico della Università di Padova

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Volume 131, 2014, pp. 237–258
DOI: 10.4171/RSMUP/131-14

Published online: 2014-06-08

Localizations of tensor products

Manfred Dugas[1], Kelly Aceves[2] and Bradley Wagner[3]

(1) Baylor University, Waco, USA
(2) Baylor University, Waco, USA
(3) Baylor University, Waco, USA

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.

Keywords: Torsion-free abelian groups, tensor products, localizations

Dugas Manfred, Aceves Kelly, Wagner Bradley: Localizations of tensor products. Rend. Sem. Mat. Univ. Padova 131 (2014), 237-258. doi: 10.4171/RSMUP/131-14