Abstract
Let A be commutative Noetherian ring of dimension d. In this paper we show that every finitely generated projective \(A[X_1, X_2, \ldots , X_r]\)-module of constant rank n is generated by \(n+d\) elements. We also extend some results over the Laurent polynomial ring \(A[X,X^{-1}]\), which are true for polynomial rings.
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Acknowledgements
Funding to SK Upadhyay was provided by Council of Scientific and Industrial Research (Grant No. 09/1032(0001)/2010-EMR-I).
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This work is supported by Council of Scientific and Industrial Research, Govt. of India.
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Upadhyay, S.K., Kumar, S.D. & Sridharan, R. Projective Modules and Efficient Generation of Ideals Over Laurent Polynomial Rings. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 87, 349–353 (2017). https://doi.org/10.1007/s40010-017-0381-6
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DOI: https://doi.org/10.1007/s40010-017-0381-6