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)



Generating ideals up to projective equivalence

Author: D. Katz
Journal: Proc. Amer. Math. Soc. 120 (1994), 79-83
MSC: Primary 13E15; Secondary 13C15
MathSciNet review: 1176070
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: It is shown that every ideal in a commutative Noetherian ring of dimension $ d$ is projectively equivalent to an ideal having $ d + 1$ generators.

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

  • [1] H. Boratynski, Generating ideals up to radical, Arch. Math. 33 (1979), 423-425. MR 567361 (82a:13004)
  • [2] D. Eisenbud and E. G. Evans, Jr., Every algebraic set in $ n$-space is the intersection of $ n$ hypersurfaces, Invent. Math. 19 (1973), 107-112. MR 0327783 (48:6125)
  • [3] N. Mohan Kumar, On two conjectures about polynomial rings, Invent. Math. 40 (1978), 225-236. MR 499785 (80c:13010)
  • [4] E. Kunz, Introduction to commutative algebra and algebraic geometry, Birkhäuser, Boston, MA, 1985. MR 789602 (86e:14001)
  • [5] G. Lyubesnik, A property of ideals in polynomial rings, Proc. Amer. Math. Soc. 98 (1986), 399-400. MR 857929 (87k:13010)
  • [6] S. McAdam, Finite covering by ideals, Ring Theory (Proceedings of the Oklahoma Conference), Lecture Notes in Pure and Appl. Math., vol. 7, Marcel Dekker, New York, 1974, pp. 163-171. MR 0332749 (48:11075)
  • [7] -, Asymptotic prime divisor, Lectures Notes in Math., vol. 1023, Springer, Berlin, 1983. MR 722609 (85f:13018)
  • [8] D. G. Northcott and D. Rees, Reductions of ideals in local rings, Math. Proc. Cambridge Philos. Soc. 50 (1954), 145-158. MR 0059889 (15:596a)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13E15, 13C15

Retrieve articles in all journals with MSC: 13E15, 13C15

Additional Information

Keywords: Projectively equivalent ideals
Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society