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<div><span class="kw">theorem </span><a NAME="T42"><span class="comment"><font color="firebrick">:: IDEAL_2:42</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">p</font> being   <a href="ring_1.html#V2" title="RING_1:attr.2">prime</a>  <a href="ideal_1.html#NM1" title="IDEAL_1:NM.1">Ideal</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">q</font> being   <a href="ideal_1.html#NM1" title="IDEAL_1:NM.1">Ideal</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b4">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b3">q</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ideal_2.html#K6" title="IDEAL_2:func.6">PRIMARY</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">p</font>) &amp;  not <font color="Olive" title="b4">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b3">q</font> holds <br/><font color="Olive" title="b3">q</font> <a href="ideal_1.html#K16" title="IDEAL_1:func.16">%</a> <span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b4">x</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="ideal_1.html#K7" title="IDEAL_1:func.7">-Ideal</a></span>)</span> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a>  <a href="ideal_2.html#K6" title="IDEAL_2:func.6">PRIMARY</a> (<font color="Olive" title="b1">A</font>,<font color="Olive" title="b2">p</font>)</div></div>
