Cancellation problem for projective modules over affine algebras

Details Cancellation problem for projective modules over affine algebras Cancellation problem for projective modules over affine algebras

2007-08-22

arxiv.org/abs/0708.2961v1

Journal of K Theory 3 (2009), 561-581

Mathematics

Commutative Algebra

16 pages

Scientific paper

Let A be a ring of dimension d and let P be a projective A-module of rank d. We prove that if for every finite extension R of A, R^d is cancellative, then P is cancellative. This gives an alternate proof of Bhatwadekar's result: every projective module of rank d over an affine algebra of dimension d over a C_1-field of characteristic 0 is cancellative. Let P be a projective module of rank d-1 over an affine agebra of dimension d over an algebraically closed field. Then, it is not known if P is cancellative. We prove some results in this direction also.

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