The double centralizer of the \(\sigma\)-injective hull (Q795145)

\textit{J. Lambek} [Lectures on rings and modules (1966; Zbl 0143.264)] has proved that for any ring R the double centralizer of the injective hull of \(R_ R\) is a ring of right quotients of R. In this paper we generalize his result to the \(\sigma\)-injective hull as follows: If \(\sigma\) is any idempotent kernel functor on Mod-R and \(\eta\) the Lambek radical. If \(\sigma '=\sigma \cap \eta\), then the double centralizer of the \(\sigma\)-injective hull of \(R_ R\) is isomorphic to the ring of right quotients of R with respect to \(\sigma\) '.