Interior and closure operators on residuated ordered semigroup(剩余序半群的内部和闭包算子)

In this paper, the concept of inner and closure operators on residuated ordered semigroups is introduced, some of their related algebraic properties are studied. Further the relationship between weak inner and strong closure operators on residuated ordered semigroups is explored, and a method for their mutual transformation is obtained. Meanwhile, the relationship between the set of internal operators and the set of closure operators on the residuated ordered semigroup is discussed, it is proved that a Galois adjoint pair can be established between this two sets. Finally, the characterization of internal and closure operators on some related algebraic structure of residuated ordered semigroup is given.通过引入剩余序半群的内部和闭包算子概念，研究了相关代数性质，讨论了剩余序半群内部和闭包算子之间的关系，得到了两者相互转化的方法。同时，讨论了剩余序半群内部和闭包算子集之间的关系，证明了两者之间可以建立伽罗瓦伴随对，给出了剩余序半群相关代数结构内部和闭包算子的刻画。