http://www.mathematik.uni-kl.de/~zca/Reports_on_ca/02/paper_html/node27.html
What is the algorithm to calculate the kernel of a module as defined in the link above?
According to my understanding, after reading "A Singular Introduction to Commutative Algebra", the kernel is some sort of elimination algorithm, but I don't really understand it.
In the link above, I don't understand $R^r \xrightarrow{A} R^m/Im(B)$ where $A$ and $B$ are polynomial matrices.
In particular, I'm confused about $Im(B)$ which is the image of the zeros (roots) of $B$: substituting a root of $B$ into $B$ makes $B$ zero and then $Im(B)$ would be zero, too.
Thanks for your help.