I know about ring homomorphism and some properties of ring. I got stuck into a problem which was asked in TIFR 19. The number of ring homomorphisms from $\mathbb{Z}[x,y]$ to $\mathbb{F}_2[x]/(x^3+x^2+x+1)$ is __ ? Please help me. Thank in advance.
2026-04-08 09:21:09.1775640069
How to find number of ring homomorphism?
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How to get started: A ring homomorphism is uniquely defined by where it sends a set of generators for the domain. The domain here is $\Bbb Z[x, y]$ and a set of generators is $\{1, x, y\}$. How many possibilities are there for where you can send those three elements?