摘要
研究结合环范畴中的半遗传对偶根,证明了如果存在一个特征为零的单环是一个R-根环,则半遗传对偶根R是一个遗传根;如果存在两个不同的素数p和q,使得p阶加群上的零环和q阶加群上的零环都是R-根环,则半遗传对偶根R是一个超幂零根.由此导出非遗传的半遗传根成为对偶根的一个必要条件。
The semihereditary radical was studied, it is proved that a semihereditary dual radical R is hereditary if there exists a simple ring of characteristic zero such that it is an R—radical ring. It is also proved that a semihereditary dual radical R is supernilpotent if there exist two prime numbers p and q such that the zero ring over the cyclic additive group of order p or q is an R-radical ring.
关键词
结合环
半遗传根
对偶根
Associative ring
Scmihcreditary radical
Dual radical
