Let S be a distributive {∨, 0 }-semilattice. In a previous paper, the second author proved the following result: Suppose that S is a lattice. Let K be a lattice, let φ : Conc K → S be a {∨, 0 }-homomorphism. Then φ is, up to isomorphism, of the form Conc f , for a lattice L and a lattice homomorphism f : K → L. In the statement above, Conc K denotes as usual the {∨, 0 }-semilattice of all finit...

‎We give a simple and independent axiomatization of reticulations on residuated lattices‎, ‎which were axiomatized by five conditions in [C‎. ‎Mureşan‎, ‎The reticulation of a residuated lattice‎, ‎Bull‎. ‎Math‎. ‎Soc‎. ‎Sci‎. ‎Math‎. ‎Roumanie‎ ‎51 (2008)‎, ‎no‎. ‎1‎, ‎47--65]‎. ‎Moreover‎, ‎we show that reticulations can be considered as lattice homomorphisms between residuated lattices and b...

In this paper, we study an equivalence relation on the set of fuzzysubgroups of an arbitrary group G and give four equivalent conditions each ofwhich characterizes this relation. We demonstrate that with this equivalencerelation each equivalence class constitutes a lattice under the ordering of fuzzy setinclusion. Moreover, we study the behavior of these equivalence classes under theaction of a...

In this paper, we attempt to formalize a novel approach to the syncretic argumentation, which allows agents with different epistemology to engage in argumentation, taking into account the Golden Rule in the ethics of reciprocity and Confucius’ Golden Rule. We address this new argumentation framework in two ways. One is by introducing the lattice homomorphism on truth-values (epistemic states) o...

Stone algebras have been characterized by Chen and Grätzer in terms of triples (B;D;'), whereD is a distributive lattice with 1; B is a Boolean algebra, and ' is a bounded lattice homomorphism from B into the lattice of …lters of D: If D is bounded, the construction of these characterizing triples is much simpler, since the homomorphism ' can be replaced by one from B into D itself. The triple ...

Let L1 be a finite lattice with an ideal L2. Then the restriction map is a {0, 1}-homomorphism from ConL1 into ConL2. In 1986, the present authors published the converse. If D1 and D2 are finite distributive lattices, and φ : D1 → D2 is a {0, 1}-homomorphism, then there are finite lattices L1 and L2 with an embedding η of L2 as an ideal of L1, and there are isomorphisms ε1 : ConL1 → D1 and ε2 :...

The aim of this paper is to study the actions of the groups on lattices and to give some connections between the structure of a group and the structure of its subgroup lattice. Moreover, we shall introduce the concept of direct ∨-sum of G-sublattices and we shall present a generalization of a result about finite nilpotent groups. 1 Preliminaries Let (G, ·, e) be a monoid and L be a G–set (relat...

In the early eighties, A. Huhn proved that if D, E are finite distributive lattices and ψ : D → E is a {0}-preserving join-embedding, then there are finite lattices K, L and there is a lattice homomorphism φ : K → L such that ConK (the congruence lattice of K) is isomorphic to D, ConL (the congruence lattice of L) is isomorphic to E, and the natural induced mapping extφ : ConK → ConL represents...