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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On prime ideals with generic zero $ x\sb{i}=t\sp{n\sb{i}}$


Author: H. Bresinsky
Journal: Proc. Amer. Math. Soc. 47 (1975), 329-332
MSC: Primary 14H05; Secondary 13A15
MathSciNet review: 0389912
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Abstract: Let $ {n_i},1 \leq i \leq r,r \geq 3$, be natural numbers such that $ ({n_1}, \cdots ,{n_r}) = 1$ and $ {n_i} = \Sigma _{j = 1}^r{z_j}{n_j},{z_j}$. nonnegative integers, implies $ {z_j} = 0,j \ne i$, and $ {z_i} = 1$. It is shown that for prime ideals with generic zero $ {x_i} = {t^{{n_i}}}$ and $ r \geq 4$, arbitrary large finite minimal sets of generators exist.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1975-0389912-0
PII: S 0002-9939(1975)0389912-0
Article copyright: © Copyright 1975 American Mathematical Society