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- Jun 22, 2012
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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: [TEX] k[x, x^2y, x^3y^2, ... ... ... \ , x^iy^{i-1} ... ... ] [/TEX] 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
[Note: This has also been posted on MHF]
Exercise 10 reads as follows:
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Prove that the subring: [TEX] k[x, x^2y, x^3y^2, ... ... ... \ , x^iy^{i-1} ... ... ] [/TEX] 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
[Note: This has also been posted on MHF]
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