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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="group_1.html#V7">commutative</a> non <a href="vectsp_1.html#V10">degenerated</a> <a href="vectsp_2.html#V2">domRing-like</a> <a href="funcsdom.html#NM1">Ring</a>;<br/>

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for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> holds <font color="Olive">b<sub>1</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="group_1.html#K1">*</a> <font color="Olive">b<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="quofield.html#E61"><i><font color="Green">Lemma51</font></i></a></i>;<br/>
<b>hence </b><a NAME="E2:64"/>
 <a href="quofield.html#K21" target="_self">the_Field_of_Quotients</a> <font color="Maroon">c<sub>1</sub></font> is  non <a href="struct_0.html#V3">empty</a> <a href="group_1.html#V7">commutative</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a> 
 <b>by </b><i><a class="ref" href="group_1.html#D16">GROUP_1:def 16</a></i>;<br/>


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