## Noetherian Rings - Dummit and Foote - Chapter 15 - exercise 10

I am reading Dummit and Foote Chapter 15, Section 15.1: Noetherian Rings and Affine Algebraic Sets.

Prove that the subring: $k[x, x^2y, x^3y^2, ... ... ... \ , x^iy^{i-1} ... ... ]$ of the polynomial ring k[x,y] is not a Noetherian ring and hence not a finitely generated k-algebra.