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\({L_k}\)-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
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