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Cancellation problem for projective modules over affine algebras

Published online by Cambridge University Press:  14 November 2008

Manoj Kumar Keshari
Manoj Kumar Keshari
Affiliation:
Department of Mathematics, Indian Institute of Technology Mumbai, Mumbai - 400076, India, [email protected].
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Abstract

Let A be an affine algebra of dimension n over an algebraically closed field k with 1/n! ∈ k. Let P be a projective A-module of rank n − 1. Then, it is an open question due to N. Mohan Kumar, whether P is cancellative. We prove the following results:

(i) If A = R[T,T−1], then P is cancellative.

(ii) If A = R[T,1/f] or A = R[T,f1/f,…,fr/f], where f(T) is a monic polynomial and f,f1,…,fr is R[T]-regular sequence, then An−1 is cancellative. Further, if k = p, then P is cancellative.

Keywords

projective modulesaffine domaincancellation problem
Type
Research Article
Information
Journal of K-Theory , Volume 3 , Issue 3 , June 2009 , pp. 561 - 581
Copyright
Copyright © ISOPP 2009

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