\({L_k}\)-prime closure operators and \({L_k}\)-prime interior operators on \(L\)-partially ordered sets. (Chinese. English summary) Zbl 1438.06003

Xu, Kuankuan; Lu, Tao

Fuzzy Syst. Math. 33, No. 2, 19-22 (2019).

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

Keywords:

\(L\)-partially ordered sets; \({L_k}\)-prime closure operators; \({L_k}\)-prime interior operators