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<div><span class="kw">theorem </span><a NAME="T7"><span class="comment"><font color="firebrick">:: RINGFRAC:7</font></span><br/></a><div class="add"> 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">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">A</font><br/>  for <font color="Olive" title="b3">J</font> being   <a href="subset_1.html#V1" title="SUBSET_1:attr.1">proper</a>  <a href="ideal_1.html#NM1" title="IDEAL_1:NM.1">Ideal</a> of <font color="Olive" title="b1">A</font> holds   <a href="topzari1.html#K2" title="TOPZARI1:func.2">multClSet</a> (<font color="Olive" title="b3">J</font>,<font color="Olive" title="b2">a</font>) is  <a href="c0sp1.html#V3" title="C0SP1:attr.3">multiplicatively-closed</a>  ;<br/></div></div>
