  The universal enveloping algebra ${\mathcal U}({\widehat{\frak{gl}}_n})$ of
${\widehat{\frak{gl}}_n}$ was realized in \cite[Ch. 6]{DDF} using affine Schur
algebras. In particular some explicit multiplication formulas in affine Schur
algebras were derived. We use these formulas to study the structure of affine
Schur algebras. In particular, we give a presentation of the affine Schur
algebra ${\mathcal S}_{{\!\vartriangle}}(n,r)_{\mathbb Q}$.
