We generalize a result of Eisenbud-Huneke-Ulrich on the maximal graded shifts of a module with prescribed annihilator and prove a linear regularity bound for ideals in a polynomial ring depending only on the first $p - c$ steps in the resolution, where $p = \mathrm{pd}(S/I)$ and $c = \mathrm{codim}(I)$.

中文翻译：

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论理想和模的最大梯度转移

我们将 Eisenbud-Huneke-Ulrich 的结果推广到具有指定歼灭器的模块的最大分级位移上，并证明多项式环中理想的线性正则性界限仅取决于分辨率中的第一个 $p - c$ 步骤，其中 $ p = \mathrm{pd}(S/I)$ 和 $c = \mathrm{codim}(I)$。