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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E35">Th35</font></span>: <a NAME="T31"><span class="comment"><font color="firebrick">:: IDEAL_2:31</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">A</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">I</font> being   <a href="ideal_1.html#NM1" title="IDEAL_1:NM.1">Ideal</a> of <font color="Olive" title="b1">A</font> holds <br/> ( <font color="Olive" title="b2">I</font> is  <a href="ideal_2.html#V2" title="IDEAL_2:attr.2">primary</a>  iff (  not <font color="Olive" title="b1">A</font> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <font color="Olive" title="b2">I</font> is  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>  &amp; (  for <font color="Olive" title="b3">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">A</font> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <font color="Olive" title="b2">I</font></span>)</span>  st <font color="Olive" title="b3">x</font> is  <a href="ringfrac.html#V1" title="RINGFRAC:attr.1">zero_divisible</a>  holds <br/><font color="Olive" title="b3">x</font> is  <a href="topzari1.html#V1" title="TOPZARI1:attr.1">nilpotent</a>  ) ) )</div></div>
