Exercise 4, Appendix 0

Let A be a local ring endowed with a valuation $v_A$. Let B be a blowing-up of A. Now prove that the valuation $v_A$ extends, in a unique manner, to a valuation $v_B$ of B, and that the value groups $v_A(A)$ and $v_B(B)$ coincide. If A is a discrete valuation ring, with uniformizer $\pi$, B is also a discrete valuation ring, one of whose uniformizers is the image of $\pi$ in B.