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This restriction normally takes the shape of a homomorphism whose kernel would be the list of capabilities that are zero on , so it displays to be a quotient of .
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The geometric image is probably clearest in the case in which can be a compact Hausdorff Place which is its ring of capabilities.
At this time I'd personally lean toward the example staying right. I really just really need to see that $Y=X/sim$ is Hausdorff.
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Even though the relevance of those rings to variety principle looks questionable, the purpose here is to construct geometric play at gn math intuition. You are able to think about this post an prolonged Alternative to Work out 26 in Chapter one of Atiyah-Macdonald.
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I’m undecided. But as an alternative to go ahead and take concrete viewpoint I’d choose to mention another standard basic principle for defining an excellent Idea of homomorphism. Little insight: If you're able to understand a framework as a little class, homomorphisms really should be functors.
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