On prime ideals with generic zero $x_{i}=t^{n_{i}}$
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- by H. Bresinsky PDF
- Proc. Amer. Math. Soc. 47 (1975), 329-332 Request permission
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.References
- H. Grauert and R. Remmert, Analytische Stellenalgebren, Die Grundlehren der mathematischen Wissenschaften, Band 176, Springer-Verlag, Berlin-New York, 1971 (German). Unter Mitarbeit von O. Riemenschneider. MR 0316742, DOI 10.1007/978-3-642-65033-8
- Jürgen Herzog, Generators and relations of abelian semigroups and semigroup rings, Manuscripta Math. 3 (1970), 175–193. MR 269762, DOI 10.1007/BF01273309
- Matilde Nicolini, Sulle basi minimali di un ideale, Matematiche (Catania) 25 (1970), 174–181 (1971) (Italian). MR 304361
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 329-332
- MSC: Primary 14H05; Secondary 13A15
- DOI: https://doi.org/10.1090/S0002-9939-1975-0389912-0
- MathSciNet review: 0389912