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Euler class group of a Laurent polynomial ring: Local case

DSpace at IIT Bombay

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Title Euler class group of a Laurent polynomial ring: Local case
 
Creator KESHARI, MK
 
Subject projective-modules
generation
ideals
cancellation
elements
question
nori
projective modules
unimodular elements
euler class group
 
Description Let R be a Noetherian commutative ring of dimension n > 2 and let A = R[T, T-1]. Assume that the height of the Jacobson radical of R is at least 2. Let P be a projective A-module of rank n = dim A - 1 with trivial determinant. We define an abelian group called the "Euler class group of A," denoted by E(A). Let X be an isomorphism from A to det(P). To the pair (P, chi), we associate an element of E(A), called the Enter class of P, denoted by e(P, X). Then we prove that a necessary and sufficient condition for P to have a unimodular element is the vanishing of e(P, X) in E(A). Earlier, Bhatwadekar and Raja Sridharan have defined the Euler class group of R, denoted by E(R), and have proved similar results for projective R-module of rank n. Later, M.K. Das defined the Euler class group of the polynomial ring R[T], denoted by E(R[T]), and proved similar results for projective R[T]-modules of rank n with trivial determinant. (c) 2006
 
Publisher ACADEMIC PRESS INC ELSEVIER SCIENCE
 
Date 2011-07-12T15:12:14Z
2011-12-26T12:48:56Z
2011-12-27T05:34:29Z
2011-07-12T15:12:14Z
2011-12-26T12:48:56Z
2011-12-27T05:34:29Z
2007
 
Type Article
 
Identifier JOURNAL OF ALGEBRA, 308(2), 666-685
0021-8693
http://dx.doi.org/10.1016/j.jalgebra.2006.06.016
http://dspace.library.iitb.ac.in/xmlui/handle/10054/3362
http://hdl.handle.net/10054/3362
 
Language en