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<span class="kw">let </span><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">n</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds   <a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Olive" title="b1">n</font>,<font color="Maroon" title="c1">F</font>) is  <a href="ideal_1.html#V6" title="IDEAL_1:attr.6">Noetherian</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">F</font>) is  <a href="ideal_1.html#V6" title="IDEAL_1:attr.6">Noetherian</a> </span><br/>



<a NAME="E1:44"/>
<font color="Maroon" title="c1">F</font> is  <a href="ideal_1.html#V6" title="IDEAL_1:attr.6">Noetherian</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="hilbasis.html#T33" target="_self" title="HILBASIS:th.33">Th34</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:44"/>
 <a href="polynom1.html#K11" title="POLYNOM1:func.11">Polynom-Ring</a> (<font color="Maroon" title="c2">n</font>,<font color="Maroon" title="c1">F</font>) is  <a href="ideal_1.html#V6" title="IDEAL_1:attr.6">Noetherian</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hilbasis.html#T32" target="_self" title="HILBASIS:th.32">Th33</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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