局部几乎完全整环的几点注记

Some Remarks on Locally Almost Perfect Domains

中文关键词:  局部几乎完全整环  几乎投射模  几乎强平坦模  强Matlis余挠模

英文关键词:locally almost perfect domain  almost projective module  almost strongly flat module  strongly Matlis cotorsion module

中文摘要:

      整环$R$被称为局部几乎完全整环, 指的是对任意极大理想${\frak m}$都有$R_{{\frak m}}$是几乎完全整环. 本文利用局部完全环, 几乎投射模, 弱内射模, 几乎强平坦模和强Matlis余挠模给出了局部几乎完全整环的若干等价刻画.

英文摘要:

      An integral domain $R$ is called a locally almost perfect domain provided that $R_{\frak m}$ is an almost perfect domain for any maximal ideal ${\frak m}$ of $R$. In this paper, we give several characterizations of locally almost perfect domains in terms of locally perfect rings, almost projective modules, weak-injective modules, almost strongly flat modules and strongly Matlis cotorsion modules.