半环的次极大理想与次极小理想  

Submaximal ideal and subminimal ideal of semiring

作　　者：陈桂英[1] 张则增[1] 

机构地区：[1]聊城大学数学科学学院,山东聊城252059

出　　处：《河南理工大学学报（自然科学版）》2008年第2期250-252,共3页Journal of Henan Polytechnic University（Natural Science）

基　　金：山东省自然科学基金资助项目(2004ZX13);聊城大学青年基金资助项目(X051017)

摘　　要：为在半环中找到一些基本理想,使得半环中每个理想都可以表示成这些基本理想的交,首先引入半环的次极大理想概念,并讨论了次极大理想的基本性质,然后证明在半环中每个真理想都可以分解成一些次极大理想的交,且每个真理想都可以分解成有限个次极大理想的交.同时,又引入半环的次极小理想的概念,并证明半环中的每个真理想也可以表示成一些次极小理想的生成,且满足降链条件的半环中每个真理想都可以表示成有限个次极小理想的交.In order to find some basic ideals in a semiring by which any ideal in the semiring can be decomposed as intersection of these ideals, the submaximal ideal of a semiring was introduced and their fundamental properties were studied. It was proved that every proper ideals of a semiring can be decomposed as intersec- tion of submaximal ideals, and each proper ideal in a semiring satisfying decreasing conditions can be decomposed as intersection of finite submaximal ideals. Mean while, the subminimal ideals of a semiring was introduced and it was proved that every proper ideal of a semiring can be represented as generation of subminimal i- deals, further, any proper ideal in a semiring satisfying decreasing conditions can be represented as generation of finite subminimal ideals.

关 键 词：半环 极大理想 次极大理想 极小理想 次极小理想 

分 类 号：O159[理学—数学]