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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="funcsdom.html#NM1" title="FUNCSDOM:NM.1">Ring</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">I</font> being  <a href="ideal_1.html#NM1" title="IDEAL_1:NM.1">Ideal</a> of <font color="Maroon" title="c1">R</font> holds <br/> ( <font color="Olive" title="b1">I</font> is  <a href="ring_1.html#V2" title="RING_1:attr.2">prime</a>  iff <font color="Maroon" title="c1">R</font> <a href="ring_1.html#NK3" title="RING_1:NK.3">/</a> <font color="Olive" title="b1">I</font> is   <a href="vectsp_2.html#NM2" title="VECTSP_2:NM.2">domRing</a> )</span><br/><span class="kw">let </span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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>  iff <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#NM2" title="VECTSP_2:NM.2">domRing</a> )</span><br/>



<span class="kw">thus </span><a NAME="E1:34"/>
( <font color="Maroon" title="c2">I</font> is  <a href="ring_1.html#V2" title="RING_1:attr.2">prime</a>  implies <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#NM2" title="VECTSP_2:NM.2">domRing</a> )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ring_1.html#T16" target="_self" title="RING_1:th.16">Th16</a>, <a class="ref" href="ring_1.html#T17" target="_self" title="RING_1:th.17">Th17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <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#NM2" title="VECTSP_2:NM.2">domRing</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/>

<span class="kw">assume </span><a NAME="E2:34"/>
<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#NM2" title="VECTSP_2:NM.2">domRing</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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/>

<span class="kw">hence </span><a NAME="E3:34"/>
( <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>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="ring_1.html#T16" target="_self" title="RING_1:th.16">Th16</a>, <a class="ref" href="ring_1.html#T17" target="_self" title="RING_1:th.17">Th17</a></span>; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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