半群的次极大理想与次极小理想  

Submaximal Ideal and Subminimal Ideal of Semigroup

作　　者：陈露[1] 

机构地区：[1]陕西理工学院数学与计算机科学系,汉中723000

出　　处：《数学理论与应用》2005年第3期107-110,共4页Mathematical Theory and Applications

基　　金：陕西理工学院科研基金项目(SLG0423)

摘　　要：在半群中引入次极大理想和次极小理想的概念,研究了它们的基本性质.证明了次极大理想的存在性,并得到如下定理,半群中每个理想可以分解成一些次极大理想的交,特别地,在满足理想降链条件的半群中,每个理想可以分解成有限个次极大理想的交,对于次极小理想,可以得到对偶的结果.In this paper, submaximal ideal and subminimal ideal of semigroup are introduced, and their fundamental properties are studied. The existence of submaximal ideal is proved,and the follow theorem is obtained ,every ideal of semigroup S can be decomposed as intersection of some submaximal ideals. Specially, in the semigroup with descending chain condition of ideals ,every ideal can be decomposed as finite intersection of submaximal ideals. The corresponding some results in subminimal ideal is dual,

关 键 词：半群 极大理想 极小理想 次极大理想 次极小理想 降链条件 分解 定理 有限 对偶 

分 类 号：O152.7[理学—数学]