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    Das, Mrinal Kanti and Ali Zinna, Md. 2015. “Strong” Euler class of a stably free module of odd rank. Journal of Algebra, Vol. 432, p. 185.


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    Fasel, J. and Srinivas, V. 2009. Chow–Witt groups and Grothendieck–Witt groups of regular schemes. Advances in Mathematics, Vol. 221, Issue. 1, p. 302.


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The Euler Class Group of a Noetherian Ring

  • S. M. Bhatwadekar (a1) and Raja Sridharan (a2)
  • DOI: http://dx.doi.org/10.1023/A:1001872132498
  • Published online: 01 June 2000
Abstract

For a commutative Noetherian ring A of finite Krull dimension containing the field of rational numbers, an Abelian group called the Euler class group is defined. An element of this group is attached to a projective A-module of rank = dimA and it is shown that the vanishing of this element is necessary and sufficient for P to split off a free summand of rank 1. As one of the applications of this result, it is shown that for any n-dimensional real affine domain, a projective module of rank n (with trivial determinant), all of whose generic sections have n generated vanishing ideals, necessarily splits off a free direct summand of rank 1.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
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