1.      For any  <i>r</i> &#8712 <i>R </i>  and any positive integer <i>n</i>, <br>
&#966(<i>nr</i>) =  <i>n</i>&#966(<i>r</i>) and 
&#966(<i>r<sup>n</sup></i>) = (&#966(<i>r</i>))<sup><i>n</i></sup>.<br>
2.      &#966(<i>A</i>)  is a subring  of <i>S</i>.<br>
3.      If <i>A</i> is an ideal and   is onto <i>S</i>, then &#966(<i>A</i>)  is an ideal  of <i>S</i>.<br>
4.      &#966<sup>-1</sup>(<i>B</i>)   is an ideal  of<i> R</i>.<br>
5.      If <i>R</i> is commutative, then &#966(<i>R</i>)  is commutative.