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)

 
 

 

Maximal ideals in polynomial rings


Author: Anthony V. Geramita
Journal: Proc. Amer. Math. Soc. 41 (1973), 34-36
MSC: Primary 13B25
DOI: https://doi.org/10.1090/S0002-9939-1973-0318123-8
MathSciNet review: 0318123
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We show that if $ R$ is a regular local ring of dimension 2 and $ A = R[X]$ then every maximal ideal of $ A$ is an ideal-theoretic complete intersection.


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

  • [1] E. Artin and J. Tate, A note on finite ring extensions, J. Math. Soc. Japan 3 (1951), 74-77. MR 13, 427. MR 0044509 (13:427c)
  • [2] D. Eisenbud and E. G. Evans, Three conjectures about modules over polynomial rings, Conference on Commutative Algebra (Lawrence, Kansas 1972), Lecture Notes in Math., vol. 311, Springer-Verlag, Berlin and New York. MR 0432627 (55:5614)
  • [3] S. Endo, Projective modules over polynomial rings, J. Math. Soc. Japan 15 (1963), 339-352. MR 27 #5808. MR 0155875 (27:5808)
  • [4] I. Kaplansky, Commutative rings, Allyn and Bacon, Boston, Mass., 1970. MR 40 #7234. MR 0254021 (40:7234)
  • [5] M. P. Murthy, Projective $ A[X]$-modules, J. London Math. Soc. 41 (1966), 453-456. MR 34 #188. MR 0200289 (34:188)
  • [6] -, Vector bundles over affine surfaces birationally equivalent to a ruled surface, Ann. of Math. (2) 89 (1969), 242-253. MR 39 #2774. MR 0241434 (39:2774)
  • [7] J.-P. Serre, Sur les modules projectifs, Sém. Dubreil-Pisot 1960/61, no. 2.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 13B25

Retrieve articles in all journals with MSC: 13B25


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0318123-8
Keywords: Number of generators, polynomial rings, maximal ideals, projective modules
Article copyright: © Copyright 1973 American Mathematical Society

American Mathematical Society