关于基本可数生成子模的扩张性(英文)

Extending Property for Essentially Countably Generated Submodules

中文关键词:  扩张模  ecg-扩张模  ecg-拟连续模

英文关键词:extending module  ecg-extending module  ecg-quasi-continuous module.

中文摘要:

      称左R-模M是ecg-扩张模,如果M的任意基本可数生成子模是M的直和因子的基本子模.在研究了ecg-扩张模的基本性质的基础上,本文证明了对于非奇异环R,所有左R-模是ecg-扩张模当且仅当所有左R-模是扩张模.同时我们还用ecg-拟连续模刻画了Noether环和Artin半单环.

英文摘要:

      We say a left R-module M is ecg-extending if every essentially countably generated submodule of M is essential in a direct summand of M. After giving some basic properties of ecg-extending modules, we show that for a nonsingular ring R, all left R-modules