Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A note on complete intersections


Author: S. M. Bhatwadekar
Journal: Trans. Amer. Math. Soc. 270 (1982), 175-181
MSC: Primary 13B25; Secondary 13F20
DOI: https://doi.org/10.1090/S0002-9947-1982-0642336-9
MathSciNet review: 642336
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ R$ be a regular local ring and let $ R[T]$ be a polynomial algebra in one variable over $ R$. In this paper the author proves that every maximal ideal of $ R[T]$ is complete intersection in each of the following cases: (1) $ R$ is a local ring of an affine algebra over an infinite perfect field, (2) $ R$ is a power series ring over a field.


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

  • [BI] Birger Iversen, Generic local structure in commutative algebra, Lecture Notes in Math., vol. 310, Springer-Verlag, Berlin, Heidelberg and New York, 1973. MR 0360575 (50:13023)
  • [D-G] E. D. Davis and A. V. Geramita, Generation of maximal ideals in polynomial rings, Trans. Amer. Math. Soc. 231 (1977), 497-505. MR 0472800 (57:12490)
  • [L] H. Lindel, On a question of Bass, Quillen and Suslin concerning projective modules over polynomial rings, preprint.
  • [L-L] H. Lindel and W. Lütkebohmert, Projective Moduln über Polynomial Erweiterungen von Potenzreihenalgebren, Arch. Math. 28 (1977), 51-54. MR 0435078 (55:8040)
  • [Mo] N. Mohan Kumar, On two conjectures about polynomial rings, Invent. Math. 46 (1978), 225-236. MR 499785 (80c:13010)
  • [Mu] M. P. Murthy, Projective $ A[X]$-modules, J. London Math. Soc. (2) 41 (1966), 453-456. MR 0200289 (34:188)
  • [S] J.-P. Serre, Sur les modules projectifs, Sem. Dubriel-Pisot, no. 2 (1960-61), Secrétariat Math., Paris, 1963. MR 28 #3911.
  • [Z-S] O. Zariski and P. Samuel, Commutative algebra. Vol. 2, Van Nostrand, Princeton, N. J., 1958. MR 0090581 (19:833e)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 13B25, 13F20

Retrieve articles in all journals with MSC: 13B25, 13F20


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0642336-9
Article copyright: © Copyright 1982 American Mathematical Society

American Mathematical Society