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<b>let </b><font color="Maroon" title="c2">I</font> be   <a href="ideal_1.html#NM1" title="IDEAL_1:NM.1">Ideal</a> of <font color="Maroon" title="c1">R</font>;<br/>

<b>assume </b><a NAME="E1:39_1_1"/><i><font color="Green" title="E24">A1</font></i>: 
( <font color="Maroon" title="c2">I</font> is <a href="ideal_1.html#V5" title="IDEAL_1:attr.5">proper</a> &amp; <font color="Maroon" title="c2">I</font> is <a href="ring_1.html#V3" title="RING_1:attr.3">quasi-maximal</a> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="ring_1.html#D4" target="_self" title="RING_1:def.4">RING_1:def 4</a><br/>

<a NAME="E2:39_1_1"/><b>then </b><i><font color="Green" title="E25">A2</font></i>: 
( <font color="Maroon" title="c1">R</font> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <font color="Maroon" title="c2">I</font> is <a href="vectsp_1.html#V10" title="VECTSP_1:attr.10">almost_left_invertible</a> &amp; not <font color="Maroon" title="c1">R</font> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <font color="Maroon" title="c2">I</font> is <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a> )
 
<b>by </b><i><a class="ref" href="ring_1.html#T16" target="_self" title="RING_1:th.16">Th16</a>, <a class="ref" href="ring_1.html#T19" target="_self" title="RING_1:th.19">Th19</a></i>;<br/>
<a NAME="E3:39_1_1"/>
for <font color="Olive" title="b1">A</font> being non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="rlvect_1.html#V4" title="RLVECT_1:attr.4">add-associative</a> <a href="rlvect_1.html#V5" title="RLVECT_1:attr.5">right_zeroed</a> <a href="rlvect_1.html#V6" title="RLVECT_1:attr.6">right_complementable</a> <a href="group_1.html#V4" title="GROUP_1:attr.4">associative</a> <a href="group_1.html#V6" title="GROUP_1:attr.6">commutative</a> <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">well-unital</a> <a href="vectsp_1.html#V8" title="VECTSP_1:attr.8">distributive</a> <a href="vectsp_1.html#NV11" title="VECTSP_1:NV.11">Field-like</a>  <a href="vectsp_1.html#L3" title="VECTSP_1:struct.3">doubleLoopStr</a>  holds  <font color="Olive" title="b1">A</font> is <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>
 
;<br/>
<a NAME="E4:39_1_1"/><b>then </b>
<font color="Maroon" title="c1">R</font> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <font color="Maroon" title="c2">I</font> is <a href="vectsp_2.html#V1" title="VECTSP_2:attr.1">domRing-like</a>
 
<b>by </b><i><a class="txt" href="ring_1.html#E2:39_1_1"><i><font color="Green" title="E25">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E5:39_1_1"/>
( <font color="Maroon" title="c2">I</font> is <a href="ideal_1.html#V5" title="IDEAL_1:attr.5">proper</a> &amp; <font color="Maroon" title="c2">I</font> is <a href="ring_1.html#V1" title="RING_1:attr.1">quasi-prime</a> )
 <b>by </b><i><a class="txt" href="ring_1.html#E1:39_1_1"><i><font color="Green" title="E24">A1</font></i></a>, <a class="ref" href="ring_1.html#T17" target="_self" title="RING_1:th.17">Th17</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="ring_1.html#D2" target="_self" title="RING_1:def.2">RING_1:def 2</a><br/>


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