论文标题
Matlis主题的同源性
Homology with the theme of Matlis
论文作者
论文摘要
Matlis证明了整体域的分数字段的许多同源性能。在本文中，我们简化并将其中一些从一维（分别等级）案例扩展到较高维度（分别有限等级）案例。例如，我们研究Ext $（ - ，\ sim）$的弱共同点属性，并使用它来呈现分裂标准。这些配备了多种应用。例如，我们计算$ \ wideHat {r} $的投射维度，并介绍Grothendieck本地化问题的一些非noetherian版本。我们构建了一类新的共依恋模块，并将Matlis的可分解性问题扩展到更高的等级。特别是，本文介绍了Matlis的Quadric $（q，q/r，\ wideHat {r}，\ Overset {\ sim} r）的基本属性。
Matlis proved a lot of homological properties of the fraction field of an integral domain. In this paper, we simplify and extend some of them from 1-dimensional (resp. rank one) cases to the higher dimensional (resp. finite rank) cases. For example, we study the weakly co-torsion property of Ext$(-,\sim)$, and use it to present splitting criteria. These are equipped with several applications. For instance, we compute the projective dimension of $\widehat{R}$ and present some non-noetherian versions of Grothendieck's localization problem. We construct a new class of co-Hopfian modules and extend Matlis' decomposability problem to higher ranks. In particular, this paper deals with the basic properties of Matlis' quadric $(Q,Q/R, \widehat{R},\overset{\sim}R).$
