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How to find the field of rational functions on whole of projective n space. This is done in hartstone Algebraic geometry Theorem 3.4 .chapter 1. But I am having difficulty in understanding the proof of Theorem 3.4 part a, and part b, (I am recently concerned with these two parts only) ,chapter 1. Can someone explain the first two part in some more details, with steps. In part a, I want the case when Y is the full space (for i believe that it will be simpler proof then). For part b , i want for general Y.

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