论文标题
在降低残留场的投影尺寸上
On the reducing projective dimension of the residue field
论文作者
论文摘要
在本文中，我们关注某些不变的模块，称为“还原不变的”，这些模块最近由Araya-Celikbas和Araya-Takahashi引入和研究。我们提出了一个问题，每个诺瑟（Noetherian）本地环的残留场是否具有有限的降低投影维度，并为大量当地戒指的问题获得肯定的答案。此外，我们构建了具有有限的射影维度的无限投影维度模块的新示例，并研究了降低尺寸的几种基本特性，尤其是局部环的局部同态性能。
In this paper we are concerned with certain invariants of modules, called reducing invariants, which have been recently introduced and studied by Araya-Celikbas and Araya-Takahashi. We raise the question whether the residue field of each commutative Noetherian local ring has finite reducing projective dimension and obtain an affirmative answer for the question for a large class of local rings. Furthermore, we construct new examples of modules of infinite projective dimension that have finite reducing projective dimension, and study several fundamental properties of reducing dimensions, especially properties under local homomorphisms of local rings.
