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<div><span class="kw">theorem </span><a NAME="T40"><span class="comment"><font color="firebrick">:: ZMODUL08:40</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="vectsp_7.html#V3" title="VECTSP_7:attr.3">free</a>   <a href="zmodul03.html#V1" title="ZMODUL03:attr.1">finite-rank</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b2">Z</font> being   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of  <a href="zmodul08.html#K2" title="ZMODUL08:func.2">DivisibleMod</a> <font color="Olive" title="b1">V</font> holds <br/> ( <font color="Olive" title="b2">Z</font> is  <a href="zmodul03.html#V2" title="ZMODUL03:attr.2">finitely-generated</a>  iff  ex <font color="Olive" title="b3">r</font> being   non  <a href="struct_0.html#V9" title="STRUCT_0:attr.9">zero</a>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <a href="gaussint.html#K11" title="GAUSSINT:func.11">F_Rat</a> st <font color="Olive" title="b2">Z</font> is   <a href="zmodul01.html#NM3" title="ZMODUL01:NM.3">Submodule</a> of  <a href="zmodul08.html#K4" title="ZMODUL08:func.4">EMbedding</a> (<font color="Olive" title="b3">r</font>,<font color="Olive" title="b1">V</font>) )</div></div>
