I'm looking for help understanding the coordinate ring. The definition I have roughly says(adsbygoogle = window.adsbygoogle || []).push({});

There is a surjection PI:k[t_1 , ... , t_n] ---> k[X] given by restricting a polynomial to X, where X is an algebraic set.

Then k[X] is called the coordinate ring.

As i understand it all this is saying is take any polynomial in k[t_1 , ... , t_n] can now only be evaluated with elements in X. So its like changing the domain of the polynomials, (this change is just a shrinking of the bigger n-dimensional space hence the word restriction)

If my understanding is right, then why is it called the coordinate ring? does this name have a special meaning/derivation?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# The coordinate ring - Algebraic geometry

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**