  Let $A$ be a finite-dimensional algebra over a field of characteristic $p>0$.
We use a functorial approach involving torsion pairs to construct embeddings of
endomorphism algebras of basic projective $A$--modules $P$ into those of the
torsion submodules of $P$. As an application, we show that blocks of both the
classical and quantum Schur algebras $S(2,r)$ and $S_q(2,r)$ are Morita
equivalent as quasi-hereditary algebras to their Ringel duals if they contain
$2p^k$ simple modules for some $k$.
