The euler class group of a Noetherian ring

Bhatwadekar, S. M. ; Sridharan, Raja (2000) The euler class group of a Noetherian ring Compositio Mathematica, 122 (2). pp. 183-222. ISSN 0010-437X

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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 = dim A 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.

Item Type:Article
Source:Copyright of this article belongs to London Mathematical Society.
Keywords:Projective Modules; Euler Class Group; Unimodular Elements
ID Code:3192
Deposited On:11 Oct 2010 10:00
Last Modified:18 May 2011 09:34

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