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

Exercise 10 reads as follows:

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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.

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Can someone please help me get a start on this exercise.

Peter