交换可剩余半群的剩余BCI-代数  

Residual BCI-algebras of the commutative residuated semigroups

作　　者：杨闻起[1] 

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《东北师大学报（自然科学版）》2015年第4期22-25,共4页Journal of Northeast Normal University(Natural Science Edition)

基　　金：陕西省自然科学基金资助项目(2010JM1016);陕西省教育厅专项基金资助项目(14JK1050)

摘　　要：引入了交换可剩余半群的剩余BCI-代数的概念并讨论了其性质,表明了交换可剩余半群与BCI-代数的关系,得到了全序半群的剩余BCI-代数是BCK-代数,序半群是平凡的当且仅当其剩余BCI-代数是p-半单的.还给出了交换可剩余半群与其剩余BCI-代数的理想和滤子之间的关系.The concept of the residual BCI-algebra of a commutative residuated semigroup is introduced and the relation between them are discussed.In addition,two conclusions are obtained as follows.One is that the residual BCI-algebra of a total semigroup is a BCK-algebra.The other is that a ordered semigroup is trivial if and only if its residual BCI-algebra is p-semisimple.Besides,the relation of its ideal and filter between the residual BCI-algebra and a commutative residuated semigroup are investigated.

关 键 词：序半群 交换可剩余半群 BCI-代数 理想 滤子 

分 类 号：O153.1[理学—数学]