关于Γ-超半群上Green关系的若干研究

Some studies on Green's relations on Γ-semihypergroups

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.