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D -posets

František Kôpka, Ferdinand Chovanec (1994)

Mathematica Slovaca

Dense subsets of ordered sets

Vítězslav Novák, Lidmila Vránová (2001)

Mathematica Bohemica

Some modifications of the definition of density of subsets in ordered (= partially ordered) sets are given and the corresponding concepts are compared.

Directoids with an antitone involution

Ivan Chajda, Miroslav Kolařík (2007)

Commentationes Mathematicae Universitatis Carolinae

We investigate -directoids which are bounded and equipped by a unary operation which is an antitone involution. Hence, a new operation can be introduced via De Morgan laws. Basic properties of these algebras are established. On every such an algebra a ring-like structure can be derived whose axioms are similar to that of a generalized boolean quasiring. We introduce a concept of symmetrical difference and prove its basic properties. Finally, we study conditions of direct decomposability of directoids...

Discriminator order algebras

Ivan Chajda (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We prove that an order algebra assigned to a bounded poset with involution is a discriminator algebra.

Distributive ordered sets and relative pseudocomplements

Josef Niederle (2006)

Discussiones Mathematicae - General Algebra and Applications

Brouwerian ordered sets generalize Brouwerian lattices. The aim of this paper is to characterize (α)-complete Brouwerian ordered sets in a manner similar to that used previously for pseudocomplemented, Stone, Boolean and distributive ordered sets. The sublattice (G(P)) in the Dedekind-Mac~Neille completion (DM(P)) of an ordered set (P) generated by (P) is said to be the characteristic lattice of (P). We can define a stronger notion of Brouwerianicity by demanding that both (P) and (G(P)) be Brouwerian....

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