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
Angeordnete affine lokale Ternärringe und angeordnete affine Klingenbergsche Ebenen
Annihilator-preserving congruence relations in distributive nearlattices
In this note we give some new characterizations of distributivity of a nearlattice and we study annihilator-preserving congruence relations.
Annihilators and ideals in distributive and modular ordered sets
Annihilators and ideals in ordered sets
Annihilators in BCK-algebras
We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra . We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice of all deductive systems on . Moreover, relative annihilators of with respect to are introduced and serve as relative pseudocomplements of w.r.t. in .
Annihilators in normal autometrized algebras
The concepts of an annihilator and a relative annihilator in an autometrized -algebra are introduced. It is shown that every relative annihilator in a normal autometrized -algebra is an ideal of and every principal ideal of is an annihilator of . The set of all annihilators of forms a complete lattice. The concept of an -polar is introduced for every ideal of . The set of all -polars is a complete lattice which becomes a two-element chain provided is prime. The -polars are characterized...
Annihilators on weakly standard BCC-algebras.
Announcements of new results
Announcements of new results