标题： 纤维乘积的典范迹及其应用 显示英文标题

标题： Canonical traces of fiber products and their applications

摘要： 我们研究了诺特环纤维积的典范迹。此外，我们将关于称为泰特类型的科恩-麦考利环的结果推广到诺特环上。作为我们关于典范迹和泰特类型诺特环的研究应用，我们计算了由非连通单纯复形产生的斯坦利-里斯纳环的典范迹。特别是，即使底层单纯复形不连通，我们也给出了一个刻画，表明对于哪些斯坦利-里斯纳环，其典范迹包含分级极大理想。 显示英文摘要

摘要： We study the canonical trace of the fiber product of Noetherian rings. Furthermore, we extend results on the class of Cohen-Macaulay rings called Teter type to Noetherian rings. As an application of our study on canonical traces and Noetherian rings of Teter type, we compute the canonical trace of the Stanley-Reisner ring arising from a non-connected simplicial complex. In particular, we provide a characterization of Stanley-Reisner rings for which the canonical trace contains the graded maximal ideal, even when the underlying simplicial complex is not connected.