An approach to solvability in orthomodular lattices
An atomic MV-effect algebra with non-atomic center
Does there exist an atomic lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question (and slightly more) is given: An example of an atomic MV-effect algebra with a non-atomic Boolean subalgebra of sharp or central elements is presented.
An embedding problem and its application in linguistics
An equational basis in four variables for the three-element tournament
An equivalence between varieties of cyclic Post algebras and varieties generated by a finite field
In this paper we give a term equivalence between the simple k-cyclic Post algebra of order p, L p,k, and the finite field F(p k) with constants F(p). By using Lagrange polynomials, we give an explicit procedure to obtain an interpretation Φ1 of the variety V(L p,k) generated by L p,k into the variety V(F(p k)) generated by F(p k) and an interpretation Φ2 of V(F(p k)) into V(L p,k) such that Φ2Φ1(B) = B for every B ε V(L p,k) and Φ1Φ2(R) = R for every R ε V(F(p k)).
An equivalency problem in discrete programming over ordered semigroups.
An extension of the Stone representation for orthomodular lattices
An extension theorem for modular measures on effect algebras
We prove an extension theorem for modular measures on lattice ordered effect algebras. This is used to obtain a representation of these measures by the classical ones. With the aid of this theorem we transfer control theorems, Vitali-Hahn-Saks, Nikodým theorems and range theorems to this setting.
An infinite antichain of permutations.
An infinite collection of absolutely convex subgroups
An introduction to the theory of -semilattices.
An investigation on hyperS-posets over ordered semihypergroups
In this paper, we define and study the hyper S-posets over an ordered semihypergroup in detail. We introduce the hyper version of a pseudoorder in a hyper S-poset, and give some related properties. In particular, we characterize the structure of factor hyper S-posets by pseudoorders. Furthermore, we introduce the concepts of order-congruences and strong order-congruences on a hyper S-poset A, and obtain the relationship between strong order-congruences and pseudoorders on A. We also characterize...
An -algebra approach to Artin’s solution of Hilbert’s Seventeenth Problem
Using lattice-ordered algebras it is shown that a totally ordered field which has a unique total order and is dense in its real closure has the property that each of its positive semidefinite rational functions is a sum of squares.
An observation on Krull and derived dimensions of some topological lattices
Let , be an algebraic lattice. It is well-known that with its topological structure is topologically scattered if and only if is ordered scattered with respect to its algebraic structure. In this note we prove that, if is a distributive algebraic lattice in which every element is the infimum of finitely many primes, then has Krull-dimension if and only if has derived dimension. We also prove the same result for , the set of all prime elements of . Hence the dimensions on the lattice...
An order topology for finitely generated free monoids.
An ordered structure of pseudo-BCI-algebras
In Chajda's paper (2014), to an arbitrary BCI-algebra the author assigned an ordered structure with one binary operation which possesses certain antitone mappings. In the present paper, we show that a similar construction can be done also for pseudo-BCI-algebras, but the resulting structure should have two binary operations and a set of couples of antitone mappings which are in a certain sense mutually inverse. The motivation for this approach is the well-known fact that every commutative BCK-algebra...
An orthogonality-based classification of conjectures in ortholattices.
A mathematical model for conjectures (including hypotheses, consequences and speculations), was recently introduced, in the context of ortholattices, by Trillas, Cubillo and Castiñeira (Artificial Intelligence 117, 2000, 255-257). The aim of the present paper is to further clarify the structure of this model by studying its relationships with one of the most important ortholattices' relation, the orthogonality relation. The particular case of orthomodular lattices -the framework for both Boolean...
An up-spectral space need not be -spectral.
Analyse hiérarchique des préférences et généralisations de la transitivité
Angeordnete affine Klingenbergsche Ebenen