Directly indecomposable direct factors of a lattice
In this paper we generalize a result of Libkin concerning direct product decompositions of lattices.
Directoid groups
We continue the study of directoid groups, directed abelian groups equipped with an extra binary operation which assigns an upper bound to each ordered pair subject to some natural restrictions. The class of all such structures can to some extent be viewed as an equationally defined substitute for the class of (2-torsion-free) directed abelian groups. We explore the relationship between the two associated categories, and some aspects of ideals of directoid groups.
Directoids with an antitone involution
We investigate -directoids which are bounded and equipped by a unary operation which is an antitone involution. Hence, a new operation can be introduced via De Morgan laws. Basic properties of these algebras are established. On every such an algebra a ring-like structure can be derived whose axioms are similar to that of a generalized boolean quasiring. We introduce a concept of symmetrical difference and prove its basic properties. Finally, we study conditions of direct decomposability of directoids...
Directoids with sectionally antitone involutions and skew MV-algebras
It is well-known that every MV-algebra is a distributive lattice with respect to the induced order. Replacing this lattice by the so-called directoid (introduced by J. Ježek and R. Quackenbush) we obtain a weaker structure, the so-called skew MV-algebra. The paper is devoted to the axiomatization of skew MV-algebras, their properties and a description of the induced implication algebras.
Directoids with sectionally switching involutions
It is shown that every directoid equipped with sectionally switching mappings can be represented as a certain implication algebra. Moreover, if the directoid is also commutative, the corresponding implication algebra is defined by four simple identities.
Discrete minimal surface algebras.
Discrete ordered rings
Discriminator order algebras
We prove that an order algebra assigned to a bounded poset with involution is a discriminator algebra.
Discriminator varieties of Boolean algebras with residuated operators
The theory of discriminator algebras and varieties has been investigated extensively, and provides us with a wealth of information and techniques applicable to specific examples of such algebras and varieties. Here we give several such examples for Boolean algebras with a residuated binary operator, abbreviated as r-algebras. More specifically, we show that all finite r-algebras, all integral r-algebras, all unital r-algebras with finitely many elements below the unit, and all commutative residuated...
Discussion of the structure of uninorms
The paper deals with binary operations in the unit interval. We investigate connections between families of triangular norms, triangular conorms, uninorms and some decreasing functions. It is well known, that every uninorm is build by using some triangular norm and some triangular conorm. If we assume, that uninorm fulfils additional assumptions, then this triangular norm and this triangular conorm have to be ordinal sums. The intervals in ordinal sum are depending on the set of values of a decreasing...
Disjoint refinement and related topics
Disjoint sequences in Boolean algebras
We deal with the system of all sequential convergences on a Boolean algebra . We prove that if is a sequential convergence on which is generated by a set of disjoint sequences and if is any element of , then the join exists in the partially ordered set . Further we show that each interval of is a Brouwerian lattice.
Disjoint unions of incidence structures and complete lattices
Distance définie par une application monotone sur un treillis
Distance minimale entre partitions et préordonnances dans un ensemble fini
Distances between partially ordered sets
A distance between finite partially ordered sets is studied. It is a certain measure of the difference of their structure.
Distinguished completion of a direct product of lattice ordered groups
The distinguished completion of a lattice ordered group was investigated by Ball [1], [2], [3]. An analogous notion for -algebras was dealt with by the author [7]. In the present paper we prove that if a lattice ordered group is a direct product of lattice ordered groups
Distinguished extensions of an -algebra
Distinguishing subsets in lattices
Distinguishing subsets in semilattices