Let <i>R </i> be a ring and <i>A </i> be a subring of <i>R</i>.  
When is the  set of cosets {<i>r+A</i> | <i>r</i> in  <i> R</i>}  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>?