弱角环

Weakly corner rings

设R为一个环,e2=e∈R,若对于左R-模Re的每个子模N,有ReN=N,则称R的子环eRe为弱角环,e是弱角幂等元.证明了如下结果:1若R为左MC2环,则弱角环eRe也是左MC2环;2若R为左min-abel环,则弱角环eRe也是左min-abel环;3若R为左mininjective环,则弱角环eRe也是左mininjective环;4若R为左universally mininjective环,则弱角环eRe也是左universally mininjective环.

Let R be a ring with e^2=e∈R, if for any left R-submodule N of Re, ReN=N, then eRe is called the weakly corner ring of R. This paper the following results are shown： ① If R is a left MC2 ring, then so is the weakly corner ring eRe; ② If R is a left min-able ring, then so is the weakly corner ring eRe; ③ If R is a left mininjective ring, then so is the weakly corner ring ere; ④ If R is a left universally mininjective ring, then so is the weakly corner ring ere.