## $${L_k}$$-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