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<div class="ChapSects"><a href="chap4.html#X7B222197819984A6">4 <span class="Heading">Ring Maps</span></a>
<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7EBF1DD67BD0758F">4.1 <span class="Heading">Ring Maps: Attributes</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X7E7A0DE685E23202">4.1-1 KernelSubobject</a></span>
<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X82AE604486F48FC4">4.1-2 KernelEmb</a></span>
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<div class="ContSect"><span class="tocline"><span class="nocss"> </span><a href="chap4.html#X7C7401BA7E2221CB">4.2 <span class="Heading">Ring Maps: Operations and Functions</span></a>
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<span class="ContSS"><br /><span class="nocss">  </span><a href="chap4.html#X870F43DE7DDD85A3">4.2-1 Kernel</a></span>
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<h3>4 <span class="Heading">Ring Maps</span></h3>

<p><a id="X7EBF1DD67BD0758F" name="X7EBF1DD67BD0758F"></a></p>

<h4>4.1 <span class="Heading">Ring Maps: Attributes</span></h4>

<p><a id="X7E7A0DE685E23202" name="X7E7A0DE685E23202"></a></p>

<h5>4.1-1 KernelSubobject</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ KernelSubobject</code>( <var class="Arg">phi</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> submodule</p>

<p>The kernel ideal of the ring map <var class="Arg">phi</var>.</p>

<p><a id="X82AE604486F48FC4" name="X82AE604486F48FC4"></a></p>

<h5>4.1-2 KernelEmb</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ KernelEmb</code>( <var class="Arg">phi</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> map</p>

<p>The embedding of the kernel ideal <code class="code">Kernel</code><span class="SimpleMath">(</span><var class="Arg">phi</var><span class="SimpleMath">)</span> into the <code class="code">Source</code><span class="SimpleMath">(</span><var class="Arg">phi</var><span class="SimpleMath">)</span>, both viewed as modules over the ring <span class="SimpleMath">R :=</span><code class="code">Source</code><span class="SimpleMath">(</span><var class="Arg">phi</var><span class="SimpleMath">)</span> (cf. <code class="func">Kernel</code> (<a href="chap4.html#X870F43DE7DDD85A3"><span class="RefLink">4.2-1</span></a>)).</p>

<p><a id="X7C7401BA7E2221CB" name="X7C7401BA7E2221CB"></a></p>

<h4>4.2 <span class="Heading">Ring Maps: Operations and Functions</span></h4>

<p><a id="X870F43DE7DDD85A3" name="X870F43DE7DDD85A3"></a></p>

<h5>4.2-1 Kernel</h5>

<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ Kernel</code>( <var class="Arg">phi</var> )</td><td class="tdright">( method )</td></tr></table></div>
<p>Returns: a <strong class="pkg">homalg</strong> module</p>

<p>The kernel ideal of the ring map <var class="Arg">phi</var> as an abstract module.</p>


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