On reduction number of products of ideals

Dancheng Lu; Tongsuo Wu

paper

On reduction number of products of ideals

arXiv:1804.03382

Abstract

Let $R$ be a standard graded algebra over an infinite field $K$ and $M$ a finitely generated $\ZZ$-graded $R$ -module. Let $I_{1}, \dots I_{m}$ be graded ideals of $R$ . The functions $r (M / I_{1}^{a_{1}} \dots I_{m}^{a_{m}} M)$ and $r (I_{1}^{a_{1}} \dots I_{m}^{a_{m}} M)$ are investigated and their asymptotical behaviours are given. Here $r (∙)$ stands for the reduction number of a finitely graded module $∙$ .

6 pages to appear in Bulletin of the Iranian Mathematical Society