Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] H. Grauert and R. Remmert, Analytische Stellenalgebren, Springer-Verlag, Berlin-New York, 1971 (German). Unter Mitarbeit von O. Riemenschneider; Die Grundlehren der mathematischen Wissenschaften, Band 176. MR 0316742
  • [2] Jürgen Herzog, Generators and relations of abelian semigroups and semigroup rings., Manuscripta Math. 3 (1970), 175–193. MR 0269762
  • [3] Matilde Nicolini, Sulle basi minimali di un ideale, Matematiche (Catania) 25 (1970), 174–181 (1971) (Italian). MR 0304361

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 14H05, 13A15

Retrieve articles in all journals with MSC: 14H05, 13A15


Additional Information

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