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<div><span class="kw">theorem </span><a NAME="T39"><span class="comment"><font color="firebrick">:: FIELD_8:39</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font> being   <a href="vectsp_2.html#NM2" title="VECTSP_2:NM.2">domRing</a><br/>  for <font color="Olive" title="b2">S</font> being   <a href="field_4.html#NM3" title="FIELD_4:NM.3">domRingExtension</a> of <font color="Olive" title="b1">R</font><br/>  for <font color="Olive" title="b3">p</font> being   non  <a href="ratfunc1.html#NV1" title="RATFUNC1:NV.1">zero</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#K13" title="POLYNOM3:func.13">Polynom-Ring</a> <font color="Olive" title="b1">R</font></span>)</span><br/>  for <font color="Olive" title="b4">h</font> being  <font color="Olive">b<sub>1</sub></font> <a href="field_8.html#V1" title="FIELD_8:attr.1">-fixing</a>  <a href="field_8.html#NM3" title="FIELD_8:NM.3">Monomorphism</a> of <font color="Olive" title="b2">S</font> holds  <font color="Olive" title="b4">h</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="field_4.html#K1" title="FIELD_4:func.1">Roots</a> (<font color="Olive" title="b2">S</font>,<font color="Olive" title="b3">p</font>)</span>)</span> is   <a href="funct_2.html#NM2" title="FUNCT_2:NM.2">Permutation</a> of <span class="p1">(<span class="default"><a href="field_4.html#K1" title="FIELD_4:func.1">Roots</a> (<font color="Olive" title="b2">S</font>,<font color="Olive" title="b3">p</font>)</span>)</span></div></div>
