有限I_-稠密子集与I_-链

Finite I_- Dense Subset and I_- Chain

文献[1]证明了半群S含有极小I-稠密子集的充要条件是S满足弱I-极小条件 在此基础上进一步证明了半群S含有有限I-稠密子集的充要条件是S满足I-链条件。

The paper[1] proved that a semigroup S contains minimal I_- dense subsets if and only if S satisfy the weak I_- minimal condition. On the basic of this result, this article proves that a semigroup S contaion finite I_- dense subsets if and only if S cannot have unstable I_- chain and give a necessary and sufficient for semigroup S being Artinian.