On Gorenstein Flat Preenvelopes of Complexes

Abstract

In this paper we show that if the class $\mathcal{B}$ of $R$-modules is closed under well ordered direct limits, then the class $\mathcal{B}$ is preenveloping in the category of $R$-modules if and only if the class $dw\mathcal{B}$ is preenveloping in the category of $R$-complexes, where $dw\mathcal{B}$ denotes the class of all complexes with all components in $\mathcal{B}$. As an immediate consequence, we get that over commutative and Noetherian rings with dualizing complexes every complex admits a Gorenstein flat preenvelope.