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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E29">Th27</font></span>: <a NAME="T27"><span class="comment"><font color="firebrick">:: HILBASIS:27</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">R</font>, <font color="Olive" title="b2">S</font> being   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="algstr_0.html#V13" title="ALGSTR_0:attr.13">right_complementable</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">right_zeroed</a>   <a href="vectsp_1.html#V4" title="VECTSP_1:attr.4">well-unital</a>   <a href="vectsp_1.html#V5" title="VECTSP_1:attr.5">distributive</a>   <a href="group_1.html#V3" title="GROUP_1:attr.3">associative</a>   <a href="algstr_0.html#L6" title="ALGSTR_0:struct.6">doubleLoopStr</a> <br/>  for <font color="Olive" title="b3">P</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Olive" title="b1">R</font>,<font color="Olive" title="b2">S</font>  st <font color="Olive" title="b3">P</font> is  <a href="quofield.html#NV5" title="QUOFIELD:NV.5">RingIsomorphism</a>  &amp; <font color="Olive" title="b1">R</font> is  <a href="ideal_1.html#V6" title="IDEAL_1:attr.6">Noetherian</a>  holds <br/><font color="Olive" title="b2">S</font> is  <a href="ideal_1.html#V6" title="IDEAL_1:attr.6">Noetherian</a> </div></div>
