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
Distributive associative near lattices
Distributive lattices have the intersection property
Distributive lattices form an important, well-behaved class of lattices. They are instances of two larger classes of lattices: congruence-uniform and semidistributive lattices. Congruence-uniform lattices allow for a remarkable second order of their elements: the core label order; semidistributive lattices naturally possess an associated flag simplicial complex: the canonical join complex. In this article we present a characterization of finite distributive lattices in terms of the core label order...
Distributive lattices whose congruence lattice is Stone.
Distributive lattices with a given skeleton
We present a construction of finite distributive lattices with a given skeleton. In the case of an H-irreducible skeleton K the construction provides all finite distributive lattices based on K, in particular the minimal one.
Distributive lattices with an additional unary operation.
Distributive lattices with an additional unary operation. (Short Communication).