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Ideals with Trivial Conormal Bundle

Published online by Cambridge University Press:  20 November 2018

A. V. Geramita  and
C. A. Weibel
A. V. Geramita
Affiliation:
Queen's University, Kingston, Ontario
C. A. Weibel
Affiliation:
Queen's University, Kingston, Ontario
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Throughout this paper all rings considered will be commutative, noetherian with identity. If R is such a ring and M is a finitely generated R-module, we shall use v(M) to denote that non-negative integer with the property that M can be generated by v(M) elements but not by fewer.

Since every ideal in a noetherian ring is finitely generated, it is a natural question to ask what v(I) is for a given ideal I. Hilbert's Nullstellensatz may be viewed as the first general theorem dealing with this question, answering it when I is a maximal ideal in a polynomial ring over an algebraically closed field.

More recently, it has been noticed that the properties of an R-ideal I are intertwined with those of the R-module I/I2.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 1 , 01 February 1980 , pp. 210 - 218
Copyright
Copyright © Canadian Mathematical Society 1980

References

1. Altman, A. and Kleiman, S., Introduction to Grothendieck duality theory, Springer Lecture Notes in Mathematics, Vol. 146 (Springer-Verlag, Berlin-Heidelberg-New York, 1970).Google Scholar
2. Bass, H., Liberation des modules projectifs sur certains anneaux de polynômes, Springer Lecture Notes in Mathematics, Vol. 431, 228–254 (Springer-Verlag, Berlin-Heidelberg-New York, 1975).Google Scholar
3. Boratynski, M., A note on the set-theoretic complete intersection ideals, J. of Algebr. 54 (1978), 1–5.Google Scholar
4. Boratynski, M., When is an ideal generated by a regular sequence﹜ J. of Algebra 57 (1979), 236–241.Google Scholar
5. Claborn, L. and Fossum, R., Generalization of the notion of the class group, 111. J. of Math. 12 (1968), 228–253.Google Scholar
6. Davis, E. D. and Geramita, A. V., Efficient generation of maximal ideals in polynomial rings, T.A.M.S., Vol. 231 (1977), 497–504.Google Scholar
7. Ferrand, D., Suites régulières et intersection complète, C. R. Acad. Sci., Paris 264 (1967), A427–A428.Google Scholar
8. Milnor, J., Topology from the differentiable viewpoint (The University Press of Virginia, Charlottesville, 1965).Google Scholar
9. Mohan Kunar, N., On two conjectures about polynomial rings, Inventiones Mathematica. 46 (1978), 225–236.Google Scholar
10. Murthy, M. P., Complete intersections, Conference on Commutative Algebra, Queen's Papers in Pure and Applied Mathematics, No. 42 (1975), 137–154.Google Scholar
11. Quillen, D., Projective modules over polynomial rings, Inv. Math. 36 (1976), 166–172.Google Scholar
12. Serre, J.-P., Sur les modules projectif, Sem. Dubreil-Pisot (1960/61), No. 2.Google Scholar
13. Swan, R., Topological examples of projective modules, T.A.M.S. Vol. 230 (1977), 201–234.Google Scholar
14. Vasconcelos, V., Ideals generated by R-sequences, J. Alg. 6 (1967), 309–316.Google Scholar