Abstract
We prove the following results. (i) Let A be an affine algebra of dimension d ≥ 4 over F ¯ p (with p ≥ d ). Then all projective A -modules of rank d − 1 are cancellative. (ii) Let A be a ring of dimension d such that E d + 1 ( R ) acts transitively on Um d + 1 ( R ) for every finite extension R of A . Then for any projective A -module P of rank d , E ( A ⊕ P ) acts transitively on Um ( A ⊕ P ) .
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