On the existence of unimodular elements and cancellation of projective modules over noetherian and non-noetherian rings

Anjan Gupta

Let $R$ be a commutative ring of dimension $d$, $S=R[X]$ or $R[X,1/X]$ and $P$ a finitely generated projective $S$ module of rank $r$. Then $P$ is cancellative if $P$ has a unim…