Strict modules and homotopy modules in stable homotopy

Abstract

Let $R$ be any associative ring with unit and let $HR$ denote thecorresponding Eilenberg--Mac Lane spectrum. We show that thecategory of algebras over the monad $X\mapsto HR\wedge X$ on thehomotopy category of spectra is equivalent to the homotopycategory associated to a model category of $HR$-module spectra, ifthe ring $R$ is a field or a subring of the rationals, but not forall rings.