Regular elements in complete uniquely complemented lattices
Regular lattices
Regularity in p-algebras and p-semilattices
Regularity of residuated mappings.
Relative annihilator-preserving congruence relations and relative annihilator-preserving homomorphisms in bounded distributive semilattices
In this paper we shall study a notion of relative annihilator-preserving congruence relation and relative annihilator-preserving homomorphism in the class of bounded distributive semilattices. We shall give a topological characterization of this class of semilattice homomorphisms. We shall prove that the semilattice congruences that are associated with filters are exactly the relative annihilator-preserving congruence relations.
Relative co-annihilators in lattice equality algebras
We introduce the notion of relative co-annihilator in lattice equality algebras and investigate some important properties of it. Then, we obtain some interesting relations among -irreducible filters, positive implicative filters, prime filters and relative co-annihilators. Given a lattice equality algebra and a filter of , we define the set of all -involutive filters of and show that by defining some operations on it, it makes a BL-algebra.
Relative Pseudo-Complements, Join-Extensions, and Meet-Retractions.
Relatively free lattices
Remarks on Ideals in Join-Semilattices.
Remarks on powers of lattices
Remarks on special ideals in lattices
The author studies some characteristic properties of semiprime ideals. The semiprimeness is also used to characterize distributive and modular lattices. Prime ideals are described as the meet-irreducible semiprime ideals. In relatively complemented lattices they are characterized as the maximal semiprime ideals. -radicals of ideals are introduced and investigated. In particular, the prime radicals are determined by means of -radicals. In addition, a necessary and sufficient condition for the equality...
Remarks on subdirect representations in categories
Remarks on the sobriety of Scott topology and weak topology on posets
We give some necessary and sufficient conditions for the Scott topology on a complete lattice to be sober, and a sufficient condition for the weak topology on a poset to be sober. These generalize the corresponding results in [1], [2] and [4].
Remarque sur les treillis complets pseudo complémentes
Representation of algebraic distributive lattices with ℵ1 compact elements as ideal lattices of regular rings.
We prove the following result: Theorem. Every algebraic distributive lattice D with at most ℵ1 compact elements is isomorphic to the ideal lattice of a von Neumann regular ring R.(By earlier results of the author, the ℵ1 bound is optimal.) Therefore, D is also isomorphic to the congruence lattice of a sectionally complemented modular lattice L, namely, the principal right ideal lattice of R. Furthermore, if the largest element of D is compact, then one can assume that R is unital, respectively,...
Representation of Lattices by Equivalence Relations
Representations of finite lattices by orders on finite sets
Representations of locally distributive lattices
Representations of ordered semigroups and lattices by binary relations
Representative properties of the quasi-ordered set