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中文摘要：
设R是有零因子的交换环．环R称为弱Q0-SM环是指R满足半正则W-理想的升链条件；环R称为Q0-SM环是指R是弱Q0-SM环且若{In}是R的半正则υ-理想的降链，∩In是半正则理想，则{In}稳定．给出弱Q0-sM环的等价刻画，也给出Q0-H环，Q0-TV环的定义，并对它们的性质和它们与Q0-SM环的关系进行了讨论．然后定义了一般交换环的W-全局变换环Rw＊，并证明了R是Q0-SM环，则Rw＊也是Qo-SM环，且t-dim（Rw＊）=t-dim（R）-1．
英文摘要：
Let R be a commutative ring with zero divisors. A weak Q0-SM ring is defined to be a ring which satisfies the ascending chain condition on semiregular w-ideals. And a Q0-SM ring is defined to be a ring which satisfies the ascending chain condition on semiregular w-ideals as well as the descending chain condition on those chains of semiregular w-ideals whose intersection is semiregu- lar. The equivalent diseriptions of a weak Q0-SM ring are gived . Moreover, the definitions and properties of the w-global transformation ring Rw ＊ , the Q0-H ring and the Qo-TV ring are defined and discussed. At last, It is proved that if R is a Qo-SM ring, then Rw ＊ is al- so a Q0-SM ring and t-dim（Rw＊ ） =t-dim（R） -1.
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