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Remarks on Unimodular Rows

  • N. Mohan Kumar
  • M. Pavaman Murthy
Chapter
Part of the Developments in Mathematics book series (DEVM, volume 18)

Summary

If (a,b,c) is a unimodular row over a commutative ring A and if the polynomial \({z}^{2} + bz + ac\) has a root in A, we show that the unimodular row is completable. In particular, if 1∕2∈A and b 2−4ac has a square root in A, then (a,b,c) is completable.

Keywords

Exact Sequence Line Bundle Algebraic Group Maximal Ideal Commutative Ring 
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Notes

Acknowledgements

The first author was partially supported by a grant from the NSA.

References

  1. 1.
    R.Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, vol.52, Springer-Verlag, Berlin, 1977.Google Scholar
  2. 2.
    N.Mohan Kumar, A note on unimodular rows, J. Algebra 191 (1997), no.1, 228–234.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    A.A. Suslin, Stably free modules, Mat. Sbornik. 102 (1977), no.4, 537–550.MathSciNetGoogle Scholar
  4. 4.
    R.G. Swan and J. Towber, A class of projective modules which are nearly free, J. Algebra 36 (1975), no.3, 427–434.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer New York 2010

Authors and Affiliations

  1. 1.Department of MathematicsWashington University in St. LouisSt. LouisUSA
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA

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