主要对正则环的相关理论进行了研究，包括正则环理想上的模比较，并进一步研究了强正则环的模刻画。

The paper has researched module comparability theories about regular rings, including the module of regular rings and characterizations about modules over strongly regular rings.

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即语音前端声学处理法、正则相关分析的谱变换补偿方法和同模极点增加法。

They are acoustic front end processing, canonical correlation based on compensation method, and increase of poles method.

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再者，引进了分次半平坦模的概念，并有如下主要结果：环K是分次弱正则的当且仅当所有右K-模是分次半平坦的。

Next, the concept of graded semiflat module is introduced and proved that K is a group-graded weakly regular ring if and only if all right K-module is graded semiflat module.

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