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.
出处
《东北师大学报（自然科学版）》
CAS
CSCD
北大核心
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)
关键词
序半群
交换可剩余半群
BCI-代数
理想
滤子
ordered semigroup
commutation residuated semigroup
BCI-algebra
ideal
filter
