赋值整环上模的紧子模
On Tight Submodules of Modules over Valuation Domains
摘要：
这篇笔记提供了一个不寻常的方法来研究一类模，因为它是在研究一个赋值整环上的模范畴的一个子类。这个类远不是一个满子范畴，它甚至不是一个范畴。我们关心的是子类的模块组成的投射维数不超过一个，只承认态射的内核和cokernels也是对象在这个子类。这个类仍然是易于处理的，一些特性通常比模块类别更简单，但是丢失了许多熟悉的属性。这类模的一些结果类似于秩一离散赋值整环（其中整体维数为1）上模的结果。通过利用文献中可用的赋值域上的模的一般理论，例如[14]-[15]，该研究大大简化。我们的主要目标是建立基本特征，并仔细研究内射性，纯内射性和余挠性，但我们不希望深入研究这些性质。
英文摘要：
This note offers an unusual approach of studying a class of modules inasmuch as it is investigating a subclass of the category of modules over a valuation domain. This class is far from being a full subcategory, it is not even a category. Our concern is the subclass consisting of modules of projective dimension not exceeding one, admitting only morphisms whose kernels and cokernels are also objects in this subclass. This class is still tractable, several features are in general simpler than in module categories, but lots of familiar properties are lost. A number of results on modules in this class are similar to those on modules over rank one discrete valuation domains (where the global dimension is 1). The study is considerably simplified by taking advantage of the general theory of modules over valuation domains available in the literature, e.g. in [14]-[15]. Our main goal is to establish the basic features and have a closer look at injectivity, pure-injectivity, and cotorsionness, but we do not wish to enter into an in-depth study of these properties.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
