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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E13">lem21</font></span>: <a NAME="T13"><span class="comment"><font color="firebrick">:: REALALG3:13</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">F</font> being   <a href="vectsp_1.html#NM5" title="VECTSP_1:NM.5">Field</a><br/>  for <font color="Olive" title="b2">p</font> being    <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <font color="Olive" title="b1">F</font></span>)</span>  st  <a href="hurwitz.html#NK3" title="HURWITZ:NK.3">deg</a> <font color="Olive" title="b2">p</font> is  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  holds <br/> ex <font color="Olive" title="b3">q</font> being   <a href="ring_4.html#NV4" title="RING_4:NV.4">monic</a>   non  <a href="ring_4.html#V3" title="RING_4:attr.3">constant</a>   <a href="ring_4.html#M1" title="RING_4:mode.1">Element</a> of  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="polynom3.html#K12" title="POLYNOM3:func.12">Polynom-Ring</a> <font color="Olive" title="b1">F</font></span>)</span> st <br/>( <font color="Olive" title="b3">q</font> <a href="ring_4.html#R1" title="RING_4:pred.1">divides</a> <font color="Olive" title="b2">p</font> &amp; <font color="Olive" title="b3">q</font> is  <a href="ring_2.html#V5" title="RING_2:attr.5">irreducible</a>  &amp;  <a href="field_1.html#K1" title="FIELD_1:func.1">deg</a> <font color="Olive" title="b3">q</font> is  <a href="abian.html#NV2" title="ABIAN:NV.2">odd</a>  )</div></div>
