A ring homomorphism from <i> R </i> to <i> S </i> is a mapping &#966 from <i> R </i> to <i> S</i> with the properties <br>
&#966(<i>a + b</i>) = &#966(<i>a</i>) + &#966(<i>b</i>) and <br>
&#966(<i>ab</i>) = &#966(<i>a</i>)&#966(<i>b</i>) for all <i>a </i> and <i> b </i> in <i>R. </i>