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<span class="kw">let </span><font color="Maroon" title="c2">R</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">S</font> being  <font color="Maroon" title="c2">R</font> <a href="ring_3.html#V2" title="RING_3:attr.2">-isomorphic</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a> holds  <font color="Maroon" title="c2">R</font> is <font color="Olive" title="b1">S</font> <a href="ring_3.html#V2" title="RING_3:attr.2">-isomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">S</font> be  <font color="Maroon" title="c2">R</font> <a href="ring_3.html#V2" title="RING_3:attr.2">-isomorphic</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">R</font> is <font color="Maroon" title="c3">S</font> <a href="ring_3.html#V2" title="RING_3:attr.2">-isomorphic</a> </span><br/>



<a NAME="E1:115"/>
(  the   <a href="ring_3.html#NM2" title="RING_3:NM.2">Isomorphism</a> of <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">S</font> <a href="ring_3.html#K2" title="RING_3:func.2">"</a>  is  <a href="vectsp_1.html#V13" title="VECTSP_1:attr.13">additive</a>  &amp;  the   <a href="ring_3.html#NM2" title="RING_3:NM.2">Isomorphism</a> of <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">S</font> <a href="ring_3.html#K2" title="RING_3:func.2">"</a>  is  <a href="group_6.html#V1" title="GROUP_6:attr.1">multiplicative</a>  &amp;  the   <a href="ring_3.html#NM2" title="RING_3:NM.2">Isomorphism</a> of <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">S</font> <a href="ring_3.html#K2" title="RING_3:func.2">"</a>  is  <a href="group_1.html#V6" title="GROUP_1:attr.6">unity-preserving</a>  &amp;  the   <a href="ring_3.html#NM2" title="RING_3:NM.2">Isomorphism</a> of <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">S</font> <a href="ring_3.html#K2" title="RING_3:func.2">"</a>  is  <a href="mod_4.html#V3" title="MOD_4:attr.3">monomorphism</a>  &amp;  the   <a href="ring_3.html#NM2" title="RING_3:NM.2">Isomorphism</a> of <font color="Maroon" title="c2">R</font>,<font color="Maroon" title="c3">S</font> <a href="ring_3.html#K2" title="RING_3:func.2">"</a>  is  <a href="mod_4.html#V5" title="MOD_4:attr.5">epimorphism</a>  )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="ring_3.html#T73" target="_self" onmouseover="rs('ring_3/T73')" onmouseout="rh()">Th72</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:115"/>
<font color="Maroon" title="c2">R</font> is <font color="Maroon" title="c3">S</font> <a href="ring_3.html#V2" title="RING_3:attr.2">-isomorphic</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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