In Dummit and Foote, Chapter 15, Section 15.2 Radicals and Affine Varieties, Example 2, page 681 begins as follows:

-----------------------------------------------------------------------------------------

"The x-axis in is irreducible since it has coordinate ring

which is an integral domain."

------------------------------------------------------------------------------------------

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