| 关于Z[c~(1/2)]环 |
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| 引用本文： | 姚光同,贾璐. 关于Z[c~(1/2)]环[J]. 黑龙江大学自然科学学报, 2004, 0(3) |
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| 作者姓名： | 姚光同 贾璐 |
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| 作者单位： | 山东工商学院数学与信息科学学院，山东工商学院数学与信息科学学院 山东 烟台 264005，山东 烟台 264005 |
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| 基金项目： | 黑龙江省教委自然科学基金，山东工商学院校重点项目 |
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| 摘 要： | 给出Z[c_(1/2)]环的定义,并定义Z[c_(1/2)]环上的元素范数;讨论Z[c_(1/2)]环关于任意主理想的商环的个数,进而得到Z[c_(1/2)]中主理想是极大理想的充要条件,特别在Z[c_(1/2)]是主理想整环的条件下,得到了Z[c_(1/2)]的元素是素元的充要条件。
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| 关 键 词： | 商环 主理想 极大理想 素元 |
On Z[c~(1/2)] Ring |
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| YAO Guang-tong,JIA Lu. On Z[c~(1/2)] Ring[J]. Journal of Natural Science of Heilongjiang University, 2004, 0(3) |
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| Authors: | YAO Guang-tong JIA Lu |
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| Abstract: | The Z[c~(1/2)] ring is defined, and further, the definition of the norm of any element in Z[c~(1/2)] is provided. The number of quotient rings of Z[c~(1/2)] associated with any principal ideal is discussed. Thereby, a necessary and sufficient condition under which a principal ideal of Z[c~(1/2)] is maximal are obtained. In particular, when Z[c~(1/2)] is a principal ideal domain, a necessary and sufficient condition under which an element of Z[c~(1/2)] is prime is proved. |
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| Keywords: | quotient ring principal ideal maxmimal ideal prime element |
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