Closure operators on complete almost distributive lattices. II. (English) Zbl 1399.06034

Rao, G. C.; Undurthi, Venugopalam

Southeast Asian Bull. Math. 41, No. 1, 91-100 (2017).

Summary: In this paper, we introduce the concepts of a neutral closure operator, central closure operator, completely meet-distributive closure operator, completely join-distributive closure operator, completely distributive closure operator on a complete almost distributive lattice and derive their important properties.
For Part I see [the authors, “Closure operators on complete almost distributive lattices. I”, Int. J. Math. Arch. 5, No. 6, 119–124 (2014), http://www.ijma.info/index.php/ijma/article/view/2950].

MSC:

06D75	Other generalizations of distributive lattices
06A15	Galois correspondences, closure operators (in relation to ordered sets)
06B23	Complete lattices, completions

Keywords:

almost distributive lattice; complete almost distributive lattice; neutral closure operator; central closure operator