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
Representing lattices by homotopy groups of graphs
In this paper we represent every lattice by subgroups of free groups using the concept of the homotopy group of a graph.
Residuation Theory (Book Review by R. McFadden.
Retracts of abelian lattice ordered groups
Rotations of -lattices
In [2], J. Klimes studied rotations of lattices. The aim of the paper is to research rotations of the so-called -lattices introduced in [3] by V. Snasel.
Semi lattices whose structure lattice is distributive.
Semigroups and their lattice of congruences.
Semigroups and their lattice of congruences II.
Semigroups and their subsemigroup lattices.
Semigroups with Boolean Congruence Lattices.