么半群上作用的覆盖与纯满射
Covers of acts over monoids and pure epimorphisms
摘要：
在2001年，伊诺克著名的平坦覆盖猜想终于被证明，并且证明（在同一篇论文中提出了两种不同的证明[4]）已经引起了研究人员的极大兴趣。特别是，这些结果在许多其他类别中，特别是在加法类别中得到了改写（例如见[2]、[3]、[22]和[23]）。在2008年，Mahmoudi和Renshaw考虑了一个类似的问题，但使用了稍微不同的覆盖定义。他们证明，在一般情况下，他们的定义是不等同于以诺的，除了在投射的情况下，并留下了一些开放的问题，关于“其他”的定义。这个“其他”的定义是本文件的主题，我们试图模仿一些伊诺克的工作，一类的行为在monoid和集中在主要的强烈平坦的行为。我们希望在未来的报告中，将这项工作扩展到其他类的行为，如内射，无挠的，可分和自由。
英文摘要：
In 2001 Enoch's celebrated flat cover conjecture was finally proven and the proofs (two different proofs were presented in the same paper [4]) have since generated a great deal of interest among researchers. In particular the results have been recast in a number of other categories and in particular for additive categories (see for example [2], [3], [22] and [23]). In 2008, Mahmoudi and Renshaw considered a similar problem for acts over monoids but used a slightly different definition of cover. They proved that in general their definition was not equivalent to Enoch's, except in the projective case, and left open a number of questions regarding the `other' definition. This `other' definition is the subject of the present paper and we attempt to emulate some of Enoch's work to the category of acts over monoids and concentrate in the main on strongly flat acts. We hope to extend this work to other classes of acts, such as injective, torsion free, divisible and free, in a future report.
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