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<div>:: <span class="kw">deftheorem </span>   defines <a href="ringfrac.html#V2" title="RINGFRAC:attr.2">without_zero</a> <a onclick="hs(this)" href="javascript:()">RINGFRAC:def 4 : <br/></a><span> for <font color="Olive" title="b1">A</font> being   non  <a href="struct_0.html#V6" title="STRUCT_0:attr.6">degenerated</a>   <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a>  <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</a><br/>  for <font color="Olive" title="b2">V</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">A</font> holds <br/> ( <font color="Olive" title="b2">V</font> is  <a href="ringfrac.html#V2" title="RINGFRAC:attr.2">without_zero</a>  iff  not  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">A</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <font color="Olive" title="b2">V</font> );<br/></span></div>
