\({L_k}\)-prime closure operators and \({L_k}\)-prime interior operators on \(L\)-partially ordered sets. (Chinese. English summary) Zbl 1438.06003
Summary: This paper introduces the concept of \(L\)-partially ordered sets on complete residual lattices, and gives the concepts of \({L_k}\)-prime closure operators and \({L_k}\)-prime interior operators and characterizations on them. Then, it gives the generalization. The concepts of \(n\) multiple \({L_k}\)-prime closure operators and \(b\) multiple \({L_k}\)-prime interior operators and characterization on them are obtained.
MSC:
06A15 | Galois correspondences, closure operators (in relation to ordered sets) |
06A06 | Partial orders, general |
06A11 | Algebraic aspects of posets |