| 整群环的增广理想之幂的基底及其商群的结构 |
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| 引用本文： | 武海波,唐国平.整群环的增广理想之幂的基底及其商群的结构[J].西北大学学报,2005,35(1):3-6. |
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| 作者姓名： | 武海波 唐国平 |
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| 作者单位： | 西北工业大学数学系，陕西西安710072 |
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| 基金项目： | 国家自然科学基金资助项目(10271094) |
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| 摘 要： | 目的 计算特殊整群环的增广理想之幂的基底及确定其商群的结构。方法 通过增广理想中的关系，从生成元中找出基底元。结果 得到了该整群环的增广理想之幂的基底，进而确定了其商群的结构。结论 回答了关于此类特殊群的Karpilovsky问题。
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| 关 键 词： | 整群环 增广理想 基底 连续商群 |
| 文章编号： | 1000-274X(2005)01-0003-04 |
| 修稿时间： | 2004年5月14日 |
Basis of powers of the augmentation ideal of integer group ring and the structure of their quotient groups |
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| WU Hai-bo,TANG Guo-ping.Basis of powers of the augmentation ideal of integer group ring and the structure of their quotient groups[J].Journal of Northwest University(Natural Science Edition),2005,35(1):3-6. |
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| Authors: | WU Hai-bo TANG Guo-ping |
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| Abstract: | Aim The basis for powers of the augmentation ideal of one kind of special abelian groups is computed. Then the structure of their consecutive quotient groups is determined. Methods The basis elements can be found among the generated elements by the relations of powers of the augmentation ideal.Results A basis for the powers of the augmentation ideal is found and the structure of quotient groups is established.Conclusion The results answered an open problem of Karpilovsky for this special kind of groups. |
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| Keywords: | integral group ring augmentation ideal basis consecutive quotient |
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