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 are ecg- extending if and only if all left R-modules are extending. We also characterize noetherian rings and artinian semisimple rings via ecg-quasi-continuous modules.
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.
基金
the National Natural Science Foundation of China (10171082)the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, P.R.C.
