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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>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">I</font> is <a href="ring_1.html#V4" title="RING_1:attr.4">maximal</a> implies <font color="Maroon" title="c2">I</font> is <a href="ring_1.html#V2" title="RING_1:attr.2">prime</a> )</span><br/>

<b>assume </b><a NAME="E1:38_1_1"/><i><font color="Green" title="E24">A1</font></i>: 
( <font color="Maroon" title="c2">I</font> is <a href="subset_1.html#V1" title="SUBSET_1:attr.1">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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">I</font> is <a href="ring_1.html#V2" title="RING_1:attr.2">prime</a></span><br/>

<a NAME="E2:38_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="algstr_0.html#V33" title="ALGSTR_0:attr.33">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="E3:38_1_1"/>
<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="#E2:38_1_1"><i><font color="Green" title="E25">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:38_1_1"/>
( <font color="Maroon" title="c2">I</font> is <a href="subset_1.html#V1" title="SUBSET_1:attr.1">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="#E1:38_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> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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