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<head><title>kernel and image of a ring map</title>
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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_substitution_spand_spmaps_spbetween_springs.html" title="">substitution and maps between rings</a> > <a href="_kernel_spand_spimage_spof_spa_spring_spmap.html" title="">kernel and image of a ring map</a></div>
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<div><h1>kernel and image of a ring map</h1>
<div>The kernel and image of a ring map can be computed using <a href="_image.html" title="image of a map">image</a> and <a href="_kernel.html" title="kernel of a ringmap, matrix, or chain complex">kernel</a> . The output of <tt>ker</tt> is an ideal and the output of <tt>image</tt>is a ring or quotient ring.<table class="examples"><tr><td><pre>i1 : R = QQ[x,y,w]; U = QQ[s,t,u]/ideal(s^2);</pre>
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<tr><td><pre>i3 : H = map(U,R,matrix{{s^2,t^3,u^4}})
3 4
o3 = map(U,R,{0, t , u })
o3 : RingMap U <--- R</pre>
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<tr><td><pre>i4 : ker H
o4 = ideal(x)
o4 : Ideal of R</pre>
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