The  set of cosets {<i>r+A</i> | <i>r</i> in  <i> R</i>}  is a ring
under the operations (<i>s+A</i>) + (<i>t+A</I>) = <i>s+t+A</i>
and (<i>s+A</I>)(<i>t+A</I>) = <i>st + A</i>
if and only if <i>A</i> is an ideal of <i>R</i>.