\title{A Note on Cellular Approximations and Torsion Theory}
\author{Shoham Shamir}
\address{Department of Pure Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH}
\begin{abstract}
Let $R$ be a ring and $A$ a dg-$R$-module. The inclusion functor of the 
localizing subcategory generated by $A$ into the derived category of $R$ has
a right adjoint, denoted $\cell_A$. In~\cite{Benson}, Benson shows how to
compute $\cell_A R$ when $A$ is a simple module and $R$ is an Artinian ring.
We generalize this construction to the case where $A$ is the direct sum of
all cyclic torsion modules for some hereditary torsion theory $\tc$ on $R$.
In this case we assert that for every $R$-module $M$ there exists an
injective $R$-module $E$ such that:
\[ H^n(\cell_A M) \cong \ext_{\End_R(E)}^{n-1}(\hom_R(M,E),E) \text{ for }
n\geq 2\]
\end{abstract}