Manuel C. Izurdiaga

A note on the construction of finitely injective modules

We develop a technique to construct finitely injective modules which are non trivial, in the sense that they are not direct sums of injective modules. As a consequence, we prove that a ring $R$ is left noetherian if and only if each finitely injective left $R$-module is trivial, thus answering an open question posed by Salce.