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

Abstract

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 unimodular element and $r\ge d+1$. Moreover if $r\ge \dim (S)$ then $P$ has a unimodular element and therefore $P$ is cancellative. As an application we have proved that if $R$ is a ring of dimension $d$ of finite type over a Prüfer domain and $P$ is a projective $R[X]$ or $R[X,1/X]$ module of rank at least $d+1$, then $P$ has a unimodular element and is cancellative.

arXiv comment21 pages

References in corpus (1)

• Cancellation of projective modules over non-Noetherian rings

Cited by in corpus (1)

• Existence of unimodular element in a projective module over symbolic Rees algebras