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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A prime ideal in a polynomial ring whose symbolic blow-up is not Noetherian


Author: Paul C. Roberts
Journal: Proc. Amer. Math. Soc. 94 (1985), 589-592
MSC: Primary 13E15; Secondary 13A17, 13B30
DOI: https://doi.org/10.1090/S0002-9939-1985-0792266-5
MathSciNet review: 792266
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Abstract: Let $ R$ be the polynomial ring $ k[X,Y,Z]$ localized at the maximal ideal $ M = (X,Y,Z)$. We construct a prime ideal $ P$ in $ R$ which is equal to the ideal of $ m$ generic lines through the origin modulo $ {M^m}$, and we show that, for suitable choice of $ m$, the symbolic blow-up of such an ideal $ P$ is not Noetherian.


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DOI: https://doi.org/10.1090/S0002-9939-1985-0792266-5
Article copyright: © Copyright 1985 American Mathematical Society

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