Distinguishing subsets in lattices
Ivan Kopeček · Czech digital mathematics library · 1982
The present paper investigates distinguishing (also called disjunctive) subsets in relative complemented lattices and in chains.For relative complemented'lattices it appears that each singleton is distinguishing.Hence, this fact holds for special cases-complemented modular lattices and for Boolean algebras as well.The structure of distinguishing subsets in chains is described. MotivationDistinguishing (disjunctive) subsets were studied in a connection with semigroup investigation at first (B.M. Schein, M. P. Schiitzenberger, E. J. Tully Jr., [6], [8], [10]).M. Novotny and H. J. Shyr have considered distinguishing subsets in monoids from the point of view of the formal language theory ([4], [8]).J. Zapletal, H. Jurgensen and G. Thierin have investigated distinguishing subsets for some special classes of semigroups ([11], [12], [13], [2]).I. Kopedek has generalized distinguishing subsets for universal algebras ([3]).This generalization enables to study more generally defined languages (see, for instance, [5]) in a connection with the notion of distinguishing subsets and to study distinguishing subsets in other classes of algebras.In [3], the problem of the existence of distinguishing subsets in connected monounary algebras is solved.The aim of this paper is to study distinguishing subsets in lattices.