A-Verbände I
A-Verbände II
Axiom and the Simmons sublocale theorem
More precisely, we are analyzing some of H. Simmons, S. B. Niefield and K. I. Rosenthal results concerning sublocales induced by subspaces. H. Simmons was concerned with the question when the coframe of sublocales is Boolean; he recognized the role of the axiom for the relation of certain degrees of scatteredness but did not emphasize its role in the relation between sublocales and subspaces. S. B. Niefield and K. I. Rosenthal just mention this axiom in a remark about Simmons’ result. In this...
Axiomatiques et propriétés des quasi-ordres
Axiomatizing omega and omega-op powers of words
In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.
Axiomatizing omega and omega-op powers of words
In 1978, Courcelle asked for a complete set of axioms and rules for the equational theory of (discrete regular) words equipped with the operations of product, omega power and omega-op power. In this paper we find a simple set of equations and prove they are complete. Moreover, we show that the equational theory is decidable in polynomial time.
Axiomatizing quantum MV-algebras.
We introduce the notion of p-ideal of a QMV-algebra and we prove that the class of all p-ideals of a QMV-algebra M is in one-to-one correspondence with the class of all congruence relations of M.
Balanced congruences
Let V be a variety with two distinct nullary operations 0 and 1. An algebra 𝔄 ∈ V is called balanced if for each Φ,Ψ ∈ Con(𝔄), we have [0]Φ = [0]Ψ if and only if [1]Φ = [1]Ψ. The variety V is called balanced if every 𝔄 ∈ V is balanced. In this paper, balanced varieties are characterized by a Mal'cev condition (Theorem 3). Furthermore, some special results are given for varieties of bounded lattices.
Balanced d-lattices are complemented
We characterize d-lattices as those bounded lattices in which every maximal filter/ideal is prime, and we show that a d-lattice is complemented iff it is balanced iff all prime filters/ideals are maximal.
Balanced order relations on completely simple semigroups.
Banaschewski’s theorem for generalized -algebras
A generalized -algebra is called representable if it is a subdirect product of linearly ordered generalized -algebras. Let be the system of all congruence relations on such that the quotient algebra is representable. In the present paper we prove that the system has a least element.
Bases in incidence structures defined on projective spaces
Bases of minimal elements of some partially ordered free abelian groups
In the present paper, we will show that the set of minimal elements of a full affine semigroup contains a free basis of the group generated by in . This will be applied to the study of the group for a semilocal ring .
Basic pseudorings
The concept of a basic pseudoring is introduced. It is shown that every orthomodular lattice can be converted into a basic pseudoring by using of the term operation called Sasaki projection. It is given a mutual relationship between basic algebras and basic pseudorings. There are characterized basic pseudorings which can be converted into othomodular lattices.
Bell-type inequalities for parametric families of triangular norms
In recent work we have shown that the reformulation of the classical Bell inequalities into the context of fuzzy probability calculus leads to related inequalities on the commutative conjunctor used for modelling pointwise fuzzy set intersection. Also, an important role has been attributed to commutative quasi-copulas. In this paper, we consider these new Bell-type inequalities for continuous t-norms. Our contribution is twofold: first, we prove that ordinal sums preserve these Bell-type inequalities;...
Bemerkung zu der Arbeit: „Die Anwendung der Polarität auf die direkten Produktzerlegungen einer Gruppe‟ von František Šik
Bemerkung zu einer Halbgruppe der Endomorphismen auf einer einfach geordneten Menge
b-equivalent multilattices
Betweenness spaces and tree algebras
bi-BL-algebra
In this paper, we introduce the notion of a bi-BL-algebra, bi-filter, bi-deductive system and bi-Boolean elements of a bi-BL-algebra and deal with bi-filters in bi-BL-algebra. We study this structure and construct the quotient of bi-BL-algebra. Also present a classification for examples of proper bi-BL-algebras.