左极小Abel环

Left min-Abel rings

证明了如下结果:1设R为左极小Abel环,e2=e∈R满足ReR=R,则角环eRe也是左极小Abel环;2设I是R的不含幂等元的理想,且R/I是左极小Abel环,则R为左极小Abel环;3 R为左极小Abel环投射单左R-模的零化子是极大左理想.

The following results are proven： ① Let R be a left min-Abel ring and e^2= e ∈ R satisfy ReR=R, then the corner ring ere is left min-Abel ring. ② Let I be an ideal of R such that I contain no idempotents of R and R/I is left rain-Abel ring, then R is let min-Abel ring. ③ R is left rain-Abel ring if and only if the annihilator of every projective simple left R-module is maximal left ideal of R.