<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E19">Th21</font></span>: <a NAME="T18"><span class="comment"><font color="firebrick">:: IDEAL_2:18</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">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="b3">M1</font> being   <a href="ideal_1.html#NM1" title="IDEAL_1:NM.1">Ideal</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">q</font></span>)</span><br/>  for <font color="Olive" title="b4">r</font>, <font color="Olive" title="b5">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Olive" title="b1">A</font>  st <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="ring_2.html#K3" title="RING_2:func.3">canHom</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Olive" title="b3">M1</font> holds <br/><font color="Olive" title="b4">r</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Olive" title="b5">x</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1">(<span class="default"><a href="ring_2.html#K3" title="RING_2:func.3">canHom</a> <font color="Olive" title="b2">q</font></span>)</span> <a href="relset_1.html#K8" title="RELSET_1:func.8">"</a> <font color="Olive" title="b3">M1</font></div></div>
