半超群的同调理论

半超群理论在组合数学，自动机理论，模糊数学，编码理论等方面有重要的应用。半超群的同调理论采用超系研究半超群，是解决半超群的重要问题的新理论。本项目将研究以下几方面的内容：研究超系的同余的性质和S-系的同余的联系；研究超系的基本关系与S-系的进一步联系；采用S-系理论的思想研究半超群的同调理论，回答半超群目前存在的公开问题。本项目研究成果将进一步发展半超群理论，并对半超群理论的应用也具有重要意义。

Semihypergroup theory have important applications in combinatorial mathematics, automata theory, fuzzy mathematics, coding theory, etc.. Homological theory of semihypergroups investigates semihypergroups using hypersystems, which is a new theory to solve important problems of semihypergroups. This project will study the following contents. We will investigate relations between properties of congruences of hypersystems and congruences of S-acts, further relations among basic relations and S-acts. Using ideals of S-acts, we will investigate homological theory of semihypergroup and give the answer to open problems of semihypergroups. The results of this project can not only develop the theory of semihypergroups, but also have important significance for the application of theory of semihypergroups.