A proper ideal <i>A </i> of a commutative ring <i>R</i> is a <emp>maximal</emp> ideal of <i>R</i> if, whenever <i>B </i>is an ideal of <i>R</I> and
<i> A </i> is a subset of <i> B </i> and <I> B </i> is a subset of <i>R </i>, then <i>B = A</i> or <i>B = R</i>. That is, a proper ideal is maximal if 
it is not a subset of any other proper ideal.