A nonempty subset <i>S</i> of a ring <i>R</i>  is a subring of <i>R
</i> if <i>S </i> is closed under subtraction and multiplication.
That is, if <i>a-b</i> and <i>ab</i> are in <i>S
</i> whenever <i>a</i> and <i>b</i> are in <i>S</i>.