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A remark on projective modules

Published online by Cambridge University Press:  17 April 2009

Wojciech Kucharz
Wojciech Kucharz
Affiliation:
Department of Mathematics and StatisticsUniversity of New Mexico Albuquerque, New Mexico 87131, U.S.A.
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Let R denote the field of real numbers and let A be the ring of regular functions on Rn, that is the localization of R[T1 …, Tn] with respect to the set of all polynomials vanishing nowhere on Rn. Let X be an algebraic subset of Rn and let I(X) be the ideal of A of all functions vanishing on X. Assume that X is compact and nonsingular and k = codim X = 1, 2, 4 or 8. we prove here that if the A/I(X)-module I(X)/I(X)2 can be generated by k elements, then there exist a projective A-module P of rank k and a homomorphism from P onto I(X).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 3 , December 1987 , pp. 515 - 520
Copyright
Copyright © Australian Mathematical Society 1987

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