Für ${\displaystyle {}a\in A}$, ${\displaystyle {}s\in S}$ ist

${\displaystyle {}0=da=d{\left({\frac {a}{s}}\cdot s\right)}={\frac {a}{s}}ds+sd{\frac {a}{s}}=sd{\frac {a}{s}}\,.}$

Da ${\displaystyle {}s}$ eine Einheit in ${\displaystyle {}A_{S}}$ ist, folgt

${\displaystyle {}d{\frac {a}{s}}=0\,.}$