升链 meaning in English

ascending chain

It is shown that if l is a modular lattice with finite length , and with 0 , 1 the least and the largest elements in l respectively , then 1 is the union of some minimal elements in l if and only if 0 is the intersection of some maximal elements in l , if and only if each non - zero element in l is the union of some minimal elements in l . by using these results , we give the necessary and sufficient conditions of an algebra module , module , ring , group and semigroup , respectively , to be semisimple
最后得出有限生成的ps -系是noetherian ( artinian )系的充要条件是它关于本质子系满足升链(降链)条件。第二章给出了一个模格是半单的若干充要条件。得到：有有限长度的模格l上，最大元1是若干极小元的并当且仅当最小元0是若干极大元的交，当且仅当l中任意非零元可表示为若干极小元的并。