有弱局部单位半群的内射系

Injective acts over semigroups with weak local units

将幺半群的同调分类理论与S-系理论有机结合,借助酉系范畴中的内射对象研究了有弱左局部单位半群的特征.利用函子与S-系同态的可收缩性给出内射S-系的等价刻画;通过S-系上方程组的容许性质,建立S-系的内射性与其方程组的可解性之间的联系;通过探索内射系与其基本扩张的关系,给出所有S-系是内射的有弱左局部单位半群的特征.

This paper will combine homological classification of monoids with the theory of S-act, and characterize semigroups with common weak left local units by using injective S-acts in the category of unitary S-acts. By the Hom-functor and retraction of S-monomorphisms, some characterizations of injective S-acts are given. By the consistent property of systems of equations the relationship between injective S-acts and solvability of the system of equations is established. By exploring the relationship between essential extensions and injectivity, semigroups S with common weak left local units over which every left S-act is injective are characterized.