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On the number of generators of a projective module

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Abstract

In this article we give a bound on the number of generators of a finitely generated projective module of constant rank over a commutative Noetherian ring in terms of the rank of the module and the dimension of the ring. Under certain conditions we provide an improvement to the Forster–Swan bound in case of finitely generated projective modules of rank n over an affine algebra over a finite field or an algebraically closed field.

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Acknowledgements

The authors would like to thank the referee for useful remarks and suggestions. The first author sincerely thanks the Council of Scientific and Industrial Research (CSIR), Govt. of India, New Delhi for research fellowship. The second author thanks the Department of Science and Technology (DST) and National Board for Higher Mathematics (NBHM), Govt. of India for research project grant.

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Authors and Affiliations

  1. Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad, 211 004, India

    SUMIT KUMAR UPADHYAY & SHIV DATT KUMAR

  2. School of Mathematics, Tata Institute of Fundamental Research, Colaba, Mumbai, 400 005, India

    RAJA SRIDHARAN

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  1. SUMIT KUMAR UPADHYAY
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  2. SHIV DATT KUMAR
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  3. RAJA SRIDHARAN
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Correspondence to SUMIT KUMAR UPADHYAY.

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UPADHYAY, S.K., KUMAR, S.D. & SRIDHARAN, R. On the number of generators of a projective module. Proc Math Sci 123, 469–478 (2013). https://doi.org/10.1007/s12044-013-0147-2

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  • DOI: https://doi.org/10.1007/s12044-013-0147-2

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