The structure of a complete -group
The structure of an idempotent relation.
The structure of closure congruences
The structure of commutative ideal semigroups.
The structure of idempotent residuated chains
In this paper we study some special residuated lattices, namely, idempotent residuated chains. After giving some properties of Green’s relation on the monoid reduct of an idempotent residuated chain, we establish a structure theorem for idempotent residuated chains. As an application, we give necessary and sufficient conditions for a band with an identity to be the monoid reduct of some idempotent residuated chain. Finally, based on the structure theorem for idempotent residuated chains, we obtain...
The structure of linear homogeneous sets.
The structure of transitive ordered permutation groups
We give some necessary and sufficient conditions for transitive -permutation groups to be -transitive. We also discuss primitive components and give necessary and sufficient conditions for transitive -permutation groups to be normal-valued.
The study of the L-fuzzy concept lattice.
The L-Fuzzy concept theory that we have developed sets up classifications from the objects and attributes of a context through L-Fuzzy relations. This theory generalizes the formal concept theory of R. Wille. In this paper we begin with the L-Fuzzy concept definition that generalizes the definitions of the formal concept theory, and we study the lattice structure of the L-Fuzzy concept set, giving a constructive method for calculating this lattice. At the end, we apply this constructive method to...
The subalgebra lattice of a finite algebra
The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more...
The subalgebra lattice of a Heyting algebra
The sums of closed subspaces in a topological linear space
The Tensor Product of Continuous Lattices.
The tensor product of semilattices
The theory of quasi-divisors on cartesian products
The topology of continuous partially-additive monoids
The translational hull of a normal cryptogroup
The triadjoint of an orthosymmetric bimorphism
Let and be two Archimedean vector lattices and let and be their order continuous order biduals. If is a positive orthosymmetric bimorphism, then the triadjoint of is inevitably orthosymmetric. This leads to a new and short proof of the commutativity of almost -algebras.
The variety covering the variety of all modular lattices.
The word problem in the tensor product of distributive semilattices.
The zero-completion of a median algebra