O existenčných algebrách
Observables on -MV algebras and -lattice effect algebras
Effect algebras were introduced as abstract models of the set of quantum effects which represent sharp and unsharp properties of physical systems and play a basic role in the foundations of quantum mechanics. In the present paper, observables on lattice ordered -effect algebras and their “smearings” with respect to (weak) Markov kernels are studied. It is shown that the range of any observable is contained in a block, which is a -MV algebra, and every observable is defined by a smearing of a sharp...
On a cancellation rule for subdirect products of lattice ordered groups and of -algebras
On a certain construction of lattice expansions
We obtain a simple construction for particular subclasses of several varieties of lattice expansions. The construction allows a unified approach to the characterization of the subdirectly irreducible algebras
On a certain construction of MS-algebras.
On a Construction of ModularGMS-algebras
In this paper we investigate the class of all modular GMS-algebras which contains the class of MS-algebras. We construct modular GMS-algebras from the variety by means of -quadruples. We also characterize isomorphisms of these algebras by means of -quadruples.
On a construction of MS-algebras
On a homogeneity condition for -algebras
In this paper we deal with a homogeneity condition for an -algebra concerning a generalized cardinal property. As an application, we consider the homogeneity with respect to -completeness, where runs over the class of all infinite cardinals.
On a Question of J. Hashimoto
On A Random Function Defined On A Pseudo Boolean Algebra
On a Representation of Lattices by Congruence Relations
On a representation theorem of De Morgan algebras by fuzzy sets.
Once the concept of De Morgan algebra of fuzzy sets on a universe X can be defined, we give a necessary and sufficient condition for a De Morgan algebra to be isomorphic to (represented by) a De Morgan algebra of fuzzy sets.
On adjoining units to hyper-archimedean -groups
On annihilators in BL-algebras
In the paper, we introduce the notion of annihilators in BL-algebras and investigate some related properties of them. We get that the ideal lattice (I(L), ⊆) is pseudo-complemented, and for any ideal I, its pseudo-complement is the annihilator I⊥ of I. Also, we define the An (L) to be the set of all annihilators of L, then we have that (An(L); ⋂,∧An(L),⊥,0, L) is a Boolean algebra. In addition, we introduce the annihilators of a nonempty subset X of L with respect to an ideal I and study some properties...
On archimedean -algebras
On atoms in tolerance lattices of distributive lattices
On central atoms of Archimedean atomic lattice effect algebras
If element of a lattice effect algebra is central, then the interval is a lattice effect algebra with the new top element and with inherited partial binary operation . It is a known fact that if the set of central elements of is an atomic Boolean algebra and the supremum of all atoms of in equals to the top element of , then is isomorphic to a direct product of irreducible effect algebras ([16]). In [10] Paseka and Riečanová published as open problem whether is a bifull sublattice...
On central relations of complete lattices
On chains in -algebras
On complete -algebras