关于Γ-超半群上Green关系的若干研究  

Some studies on Green's relations on Γ-semihypergroups

作　　者：冯辛阳 唐剑[2] 罗彦锋[1] 

机构地区：[1]兰州大学数学与统计学院,兰州730000 [2]阜阳师范学院数学与统计学院,安徽阜阳236037

出　　处：《兰州大学学报（自然科学版）》2017年第6期837-840,共4页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(11371177);安徽省高校自然科学研究重点项目(KJ2015A161)

摘　　要：考虑了文献[9]中提出的公开问题,并通过反例给出其否定的回答.在Γ-超半群中引入了弱吸收的概念,并通过举例阐述了弱吸收Γ-超半群未必是吸收的,进而解决了文献[9]中提出的另一个问题.作为Γ-超半群的推广,引入了(*,Γ)-超半群的概念,讨论了此类超半群上的Green关系.A negative answer was given to the open problem on Green＇s relations of Γ-semihypergroups introduced in reference [9]. The concept of weakly absorbent Γ-semihypergroups was introduced, and a weakly absorbent Γ-semihypergroup is not necessarily absorbent was illustrated by an example. As an application of this result, the other problem investigated in the same paper as the above-mentioned was solved. The concept of （＊, Γ）-semihypergroups was introduced and the Green＇s relations on this class of semihypergroups were studied in detail.

关 键 词：Γ-超半群 Green关系 左(右)同余 弱吸收Γ-超半群 (＊ Γ)-超半群 

分 类 号：O152[理学—数学] O159[理学—基础数学]