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<head><title>Module ** Ring -- tensor product</title>
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<div><h1>Module ** Ring -- tensor product</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>M ** R</tt><br/><tt>R ** M</tt></div>
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<li><span>Operator: <a href="__st_st.html" title="a binary operator, usually used for tensor product or Cartesian product">**</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="___Module.html">module</a></span></span></li>
<li><span><tt>R</tt>, <span>a <a href="___Ring.html">ring</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Module.html">module</a></span>, over <tt>R</tt>, obtained by forming the tensor product of the module <tt>M</tt> with <tt>R</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>If the ring of <tt>M</tt> is a base ring of <tt>R</tt>, then the matrix presenting the module will be simply promoted (see <a href="_promote.html" title="promote to another ring">promote</a>). Otherwise, a ring map from the ring of <tt>M</tt> to <tt>R</tt> will be constructed by examining the names of the variables, as described in <tt>(map,Ring,Ring)</tt> (missing documentation<!-- tag: (map,Ring,Ring) -->).<table class="examples"><tr><td><pre>i1 : R = ZZ/101[x,y];</pre>
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<tr><td><pre>i2 : M = coker vars R
o2 = cokernel | x y |
1
o2 : R-module, quotient of R</pre>
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<tr><td><pre>i3 : M ** R[t]
o3 = cokernel | x y |
1
o3 : R[t]-module, quotient of (R[t])</pre>
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