主要讨论对左（右）理想满足半极大条件的环与对零因子满足极大条件的环的性质。

In this pater , the proterties of the rings that satisfs the semi-maximum condition for left (right) ideal and maximum condition for zero-factor are discussed.

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研究了每一个极大的右理想是拟理想的右SF -环的正则性，得到了右SF -环是正则环的一些新的刻画，推广了一些已知的结论。

We study the regularity of right SF-rings whose every maximal right ideal is a quasi-ideal. Some new characterizations on the regularity of right SF-rings are obtained, which generalize some results.

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