用模的内射性和投射性刻画环
Characterizing rings in terms of the extent of injectivity and projectivity of their modules
摘要：
给定一个环R，我们定义它的右i-轮廓（分别为）。右p剖面）是注入域（分别为投射域）的右R模。我们研究这些配置文件的晶格理论性质，并考虑如何在该属性的配置文件可能会决定环的结构，反之亦然。证明了i-轮廓同构于R的右理想的线性滤波格的一个区间，因此是模的和上原子的.特别地，我们给出了右artinian环的i-剖面的一个实用刻画。通过一个例子证明了p-轮廓不一定是集合，并刻画了右完满环的右p-轮廓.根据环的（i-或p-）轮廓来研究环的灵感来自于对没有（i-或p-）中产阶级的环的研究，这是由Er，López-Permouth和Sökmez以及Holston，López-Permouth和Orhan-Ertas最近的论文发起的。在本文中，我们得到了这些环的进一步结果，我们也使用我们的结果提供了一个特殊的QF-环类，其中任何模的内射和投射域重合的一个特征。
英文摘要：
Given a ring R, we define its right i-profile (resp. right p-profile) to be the collection of injectivity domains (resp. projectivity domains) of its right R-modules. We study the lattice theoretic properties of these profiles and consider ways in which properties of the profiles may determine the structure of rings and viceversa. We show that the i-profile is isomorphic to an interval of the lattice of linear filters of right ideals of R, and is therefore modular and coatomic. In particular, we give a practical characterization of the i-profile of a right artinian ring. We show through an example that the p-profile is not necessarily a set, and also characterize the right p-profile of a right perfect ring. The study of rings in terms of their (i- or p-)profile was inspired by the study of rings with no (i- or p-) middle class, initiated in recent papers by Er, López-Permouth and Sökmez, and by Holston, López-Permouth and Orhan-Ertas. In this paper, we obtain further results about these rings and we also use our results to provide a characterization of a special class of QF-rings in which the injectivity and projectivity domains of any module coincide.
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。
