What is $\mathbf Z[x,y]/(y+1)$ is isomorphic to?
I was wondering about this question and I think the answer must be $\mathbf{Z}[x]$. How can I show that this is isomorphic to $\mathbf{Z}[x]$? Any hints?
2026-03-29 20:55:45.1774817745
What is $\mathbf Z[x,y]/(y+1)$ isomorphic to?
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There's a homomorphism $\mathbf{Z}[x,y] \to \mathbf{Z}[x]$ mapping $f(x,y)$ to $f(x,-1)$. What are its kernel and image?