im looking for a non-noetherian ring with infinite krull dimension.would you help?
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4$\begingroup$ Take $k[x_,x_2,...]$. $\endgroup$– RalphCommented Feb 27, 2013 at 19:54
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1$\begingroup$ Take a look at this question: mathoverflow.net/questions/119627/… $\endgroup$– Neil EpsteinCommented Feb 27, 2013 at 19:54
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1 Answer
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A polynomial ring $k[X_1,X_2,\ldots]$ with an infinite number of variables will do. Finding a noetherian ring with infinite Krull dimension is harder (and first accomplished by Nagata).
answered Feb 27, 2013 at 19:34