论文标题
单一理想的饱和数量
The saturation number of monomial ideals
论文作者
论文摘要
令$ s = \ mathbb {k} [x_1，\ ldots，x_n] $是字段上的多项式环$ \ mathbb {k} $和$ \ mathfrak {m mathfrak {m} =（x_1，x_1，\ ldots，x_n）$是$ s $ s $ s $的不良exciallact maximal Ideals $。对于理想的$ i \子集s $，让$ \ mathrm {sat}（i）$是$ i \ colon \ colon \ mathfrak {m}^k = i \ colon \ colon \ colon \ mathfrak {m}^{m}^{k+1} $的最低数字$ k $。在本文中，我们计算了不可还原的单一理想及其力量的饱和数。我们将此结果应用于某些单一理想家族的普通力量和符号能力的饱和数，从这些理想的不可约合分解中出现的不可约组件的饱和数。此外，我们给出了两个变量中单元理想的饱和数的明确公式。
Let $S=\mathbb{K}[x_1,\ldots, x_n]$ be the polynomial ring over a field $\mathbb{K}$ and $\mathfrak{m}= (x_1, \ldots, x_n)$ be the irredundant maximal ideal of $S$. For an ideal $I \subset S$, let $\mathrm{sat}(I)$ be the minimum number $k$ for which $I \colon \mathfrak{m}^k = I \colon \mathfrak{m}^{k+1}$. In this paper, we compute the saturation number of irreducible monomial ideals and their powers. We apply this result to find the saturation number of the ordinary powers and symbolic powers of some families of monomial ideals in terms of the saturation number of irreducible components appearing in an irreducible decomposition of these ideals. Moreover, we give an explicit formula for the saturation number of monomial ideals in two variables.
