Unimodular elements in projective modules and an analogue of a result of mandal (Q1622009)

Let \(R\) be a commutative noetherian ring of dimension \(n\), a celebrated result due to Serre says that projective \(R\)-modules of rank \(> n\) contain a unimodular element. There are several generalization of this result for special rings. In the paper under review, the authors look for obstructions for a projective module of rank \(n\) over the above special rings to contain a unimodular element. More precisely, for a projective \(R[X_1, \cdots , X_m]\)-module of rank \(n\), \(P\), they associate an obstruction for \(P\) to split off a free summand of rank one.