BCK-代数的次极大理想  

Submaximal Ideal of the BCK Alagebra

作　　者：杨闻起[1] 

机构地区：[1]宝鸡文理学院数学系,陕西宝鸡721007

出　　处：《西南师范大学学报（自然科学版）》2004年第1期38-40,共3页Journal of Southwest China Normal University(Natural Science Edition)

摘　　要：BCK代数X的理想M称为次极大理想,如果存在x∈X-M,使得M在不含x的理想中极大.讨论了次极大理想的性质,并得到:BCK代数的每个理想都可分解为一些次极大理想的交.特别地,在满足理想降链条件的BCK代数中,每个理想都可分解为有限个次极大理想的交.An ideal M of BCKalagebra X is said to be a submaximal ideal, if there is x∈X-M, which makes M maximal in all ideals with no containning x. Some properties are discussed, and the follow theorem is obtained, every ideal of BCKalagebra X can be decomposed as intersection of some submaximal ideals. Specially, in the BCK alagebra with descending chain condition of ideals, every ideal can be decomposed as finite intersection of submaximal ideals.

关 键 词：BCK-代数 次极大理想 既约理想 降链条件 

分 类 号：O153[理学—数学]