CN-环

CN-rings

研究CN-环的一些性质,主要证明了如下结果:①设R为CN-环和左SF-环,则R为强正则环;②R为约化环当且仅当R是左NPP环和CN-环;③CN-环的次直积也是CN-环;④设R为CN-环,则R为弱reversible环,反之未必;⑤设R为CN-环,每个单奇异左R-模Wnil-内射,则R为约化环;⑥设R为CN-环,每个单奇异左R-模YJ-内射,则R为约化的弱正则环.

This paper shows the following results： ① If R is a CN-ring and left SF-ring,then R is a strongly regular ring;② R is a reduced ring if and only if R is a CN-ring and left NPP ring;③ The subdirect product of CN-rings is also a CN-ring;④ If R is a CN-ring,then R is a weakly reversible ring,but the converse is not true;⑤ If R is a CN-ring whose simple singular left modules are Wnil-injective,then R is a reduced ring;⑥ If R is a CN-ring whose simple singular left modules are YJ-injective,then R is a reduced weakly regular ring.