It is precisely the first isomorphism for rings.
Define the map: , where and
(Notice the definition of the map coincides with what we do when we take a quotient).
Find the kernel and image of this map and you're golden.
In Dummit and Foote, Chapter 15, Section 15.2 Radicals and Affine Varieties, Example 2, page 681 begins as follows:
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"The x-axis in is irreducible since it has coordinate ring
which is an integral domain."
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Can someone please help me to show formally and rigorously how the isomorphism
is established.
I suspect it comes from applying the First (or Fundamental) Isomorphism Theorem for rings ... but I am unsure of the mappings involved and how they are established
Would appreciate some help>
Peter
It is precisely the first isomorphism for rings.
Define the map: , where and
(Notice the definition of the map coincides with what we do when we take a quotient).
Find the kernel and image of this map and you're golden.