Artin半格与Noether半格  

Artin semilattice and Noether semilattice

作　　者：朱玉山[1] 

机构地区：[1]中国计量学院理学院,浙江杭州310018

出　　处：《合肥工业大学学报（自然科学版）》2005年第7期820-823,共4页Journal of Hefei University of Technology：Natural Science

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。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.

关 键 词：半格 理想 Artin半格 Noether半格 

分 类 号：O153.5[理学—数学]