On Reduction Numbers of Products of Ideals
2019
Let R be a standard graded algebra over an infinite field \(\mathbb {K}\) and M a finitely generated \({\mathbb Z}\)-graded R-module. Let \(I_1,\ldots I_m\) be graded ideals of R. The functions \(r(M/I_1^{a_1}\ldots I_m^{a_m}M)\) and \(r(I_1^{a_1}\ldots I_m^{a_m}M)\) are investigated and their asymptotical behaviours are given. Here, \(r(\bullet )\) stands for the reduction number of a finitely generated graded R-module \(\bullet \).
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