# Tagged Questions

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### On rank of a matrix whose entries are polynomials

(I took courses on linear algebra, but I don't know anything about $R$-modules or such things.) How do you define the rank of a matrix whose entries are polynomials in $K[X]$? If you assign some ...
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### The ideal $(x,y)$ is not a free $K[x,y]$-module

Given a field $K$ we have the polynomial ring $K[x,y]$ in $2$ variables, which is also a left module (over itself). How can we prove that the ideal $(x,y)$ is not a free module?
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### What is the algorithm to compute the kernel of a module homomorphism?

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, ...
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### Basis of a submodule of $\mathbb{Q}[X]^3$ over $\mathbb{Q}[X]$

I want to find the basis of a submodule of $\mathbb{Q}[X]^3$ generated by $(2X-1, X, X^2+3)$, $(X,X,X^2)$ and $(X+1,2X,2X^2-3)$. I determine that  \begin{pmatrix} 2X-1 & X & X^2+3 \\ X ...