A nonempty subset <i>A</i> of a ring <i> R</i> is an ideal of <i>R</i> if:<br>
        1. <i>a - b</i> is in  <i>A</i> whenever <i>a</i> and <i>b</i> are in <i> A</i>.<br>
        2. <i>ra</i> and <i>ar </i> are in <i>A</i> whenever <i>a</i> is in  <i>A</i>  and <i>r </i>is in <i> R</i>.