Cancellation of projective modules over polynomial extensions over a two-dimensional ring
Let \(R\) be a commutative Noetherian ring. A finitely generated projective \(R\)-module \(P\) is said to be cancellative if \(P \oplus R^n \cong Q \oplus R^n\) implies \(P \cong Q\). \textit{H. Bass} [Publ. Math., Inst. Hautes Étud. Sci. 22, 489--544 (1964; Zbl 0248.18025)] showed that every finitely generated projective \(R\)-module of rank \(> \dim(R)\) is cancellative. It followed by several researchers such as Suslin, Vaserstein, Bhatwadekar and others. To do this further, the main result of the paper is as follows: Theorem. Let \(R\) be of dimension two with \(1/2 \in R\) and let \(A = R[X_1, \ldots, X_n]\). Let \(P\) be a projective \(A\)-module of rank \(2\). Then \(P\) is cancellative if \(\bigwedge^2(P)\oplus A\) is cancellative.
scientific article; zbMATH DE number 6950428