Reduction numbers of ideals (Q1305054)

Let \(R\) be a Noetherian commutative ring with identity. For any ideal \(I\) of \(R\) the author defines the big reduction number \(\text{br}(I)\) of \(I\), and in case \(R\) is local, the reduction number \(\text{r}(I)\) of \(I\). General bounds for \(\text{br}(I)\) and \(\text{r}(I)\) in Noetherian rings for arbitrary ideals \(I\) and multiplicity bounds for \(m\)-primary ideals \(I\) in a Noetherian local ring \((R,m)\) are given.