摘要
本文从上根构造出发引进了根类的极小上生成子的概念,给出了遗传环类是根类R的极小上生成子的充分必要条件,指出了极小上生成子必须(或否)哪些环,并且哪些环可从上生成子中删掉且使上根不变。
We introduce the concept of the minimal co-generator of a radical class by the construction of upper radical. A sufficient and necessary condition for a hereditary class M of rings being the minimal co-generator of a radical class is given. Some other results are also derived. Without changing the upper radical certain rings can be deleted from the co-generator M if M is not the minimal.
关键词
根类
极小上生成子
上根
弱单环
Upper radical class
The minimal co-generator of a radical class
Weakly simple ring
Descending (ascending) chain condition for idcals
