| Artin半格与Noether半格 |
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| 引用本文： | 朱玉山.Artin半格与Noether半格[J].合肥工业大学学报(自然科学版),2005,28(7):820-823. |
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| 作者姓名： | 朱玉山 |
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| 作者单位： | 中国计量学院,理学院,浙江,杭州,310018 |
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| 摘 要： | 文章给出了半格理想的一组性质,证明了半格理想的无限交仍是该半格理想。在某种条件下,半格理想的无限并亦是该半格的理想。引入关于半格理想的极小条件、极大条件、降链条件与升链条件等有限条件,并证明了文章中所给出的有限条件在同态映射下的不变性。
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| 关 键 词： | 半格 理想 Artin半格 Noether半格 |
| 文章编号： | 1003-5060(2005)07-0820-04 |
| 修稿时间： | 2005年1月19日 |
Artin semilattice and Noether semilattice |
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| ZHU Yu-shan.Artin semilattice and Noether semilattice[J].Journal of Hefei University of Technology(Natural Science),2005,28(7):820-823. |
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| Authors: | ZHU Yu-shan |
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| Abstract: | Some properties of the ideals of a semilattice are given in this paper.Firstly,it is proved that the infinite meet for ideals of a semilattice is an ideal of the semilattice.Under certain condition, the infinite join for ideals of a semilattice is also an ideal of the semilattice.Then,some finite conditions including the minimum condition,the maximum condition,the descending chain condition,and the ascending chain condition are introduced into the ideals of a semilattice.It is proved that the minimum condition for the ideals of a semilattice is equivalent to the descending chain condition for them,and that the maximum condition for the ideals of a semilattice is equivalent to the ascendeng chain condition for them.Lastly, the invariance of the finite conditions given in this paper under homomorphism is verified. |
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| Keywords: | semilattice ideal Artin semilattice Noether semilattice |
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