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Generators of a general ideal

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A Tribute to C. S. Seshadri

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Abstract

Let R be a commutative ring and A = R[X1, …,X n ]. Let I m be the ideal generated by X1, …,X m , 0 < m < n+1, and r a positive integer. We show here that, for all (m − 1) <k < (r + 1) ,GL(k, A) acts transitively on the the set of all (f1, …, f k ) which generate I m , if and only if for all k (r + 1), all unimodular elements in Ak are completable to k × k-invertible matrices over A.

Dedicated to C.S. Seshadri for his seventieth birthday

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Authors and Affiliations

  1. The University of Chicago, Chicago, IL, 60637, USA

    M. Pavaman Murthy

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  1. M. Pavaman Murthy
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V. Lakshmibai V. Balaji V. B. Mehta K. R. Nagarajan K. Pranjape P. Sankaran R. Sridharan

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© 2003 Hindustan Book Agency

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Murthy, M.P. (2003). Generators of a general ideal. In: Lakshmibai, V., et al. A Tribute to C. S. Seshadri. Hindustan Book Agency, Gurgaon. https://doi.org/10.1007/978-93-86279-11-8_23

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