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<b>let </b><font color="Maroon">I</font> be   <a href="ideal_1.html#NM1">Ideal</a> of <font color="Maroon">R</font>;<br/>

<b>assume </b><a NAME="E1:41_1_1"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">I</font> is <a href="ideal_1.html#V5">proper</a> &amp; <font color="Maroon">I</font> is <a href="ring_1.html#V3" target="_self">quasi-maximal</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ring_1.html#D4" target="_self">RING_1:def 4</a><br/>

<a NAME="E2:41_1_1"/><b>then </b><i><font color="Green">E47</font></i>: 
( <font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font> is <a href="vectsp_1.html#V9">Field-like</a> &amp; not <font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font> is <a href="vectsp_1.html#V10">degenerated</a> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E3:41_1_1"/>
for <font color="Olive">A</font> being non <a href="struct_0.html#V3">empty</a> <a href="rlvect_1.html#V4">add-associative</a> <a href="rlvect_1.html#V5">right_zeroed</a> <a href="rlvect_1.html#V6">right_complementable</a> <a href="group_1.html#V4">associative</a> <a href="group_1.html#V7">commutative</a> <a href="vectsp_1.html#V7">distributive</a> <a href="vectsp_1.html#V8">left_unital</a> <a href="vectsp_1.html#V9">Field-like</a>  <a href="vectsp_1.html#L3">doubleLoopStr</a>  holds  <font color="Olive">A</font> is <a href="vectsp_2.html#V2">domRing-like</a>
 
;<br/>
<a NAME="E4:41_1_1"/><b>then </b>
<font color="Maroon">R</font> <a href="ring_1.html#NK3" target="_self">/</a> <font color="Maroon">I</font> is <a href="vectsp_2.html#V2">domRing-like</a>
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E5:41_1_1"/>
( <font color="Maroon">I</font> is <a href="ideal_1.html#V5">proper</a> &amp; <font color="Maroon">I</font> is <a href="ring_1.html#V1" target="_self">quasi-prime</a> )
 <b>by </b><i>, </i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ring_1.html#D2" target="_self">RING_1:def 2</a><br/>


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