Cancellation of finitely generated modules over regular rings
In this note we show that if R is a regular ring which is \(N^*\)- complete, or right or left \(\aleph_ 0\)-continuous, or left \(\aleph_ 0\)-injective, then every finitely generated right R-module cancels from direct sums if and only if R has bounded index of nilpotency (and so all primitive factor rings of R are artinian). As an application we also obtain a characterization of those polynomial rings R[x] that are semihereditary in the case that R is either \(N^*\)-complete or right or left \(\aleph_ 0\)-continuous.
scientific article; zbMATH DE number 4179575