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A completion for distributive nearlattices
The aim of this article is to propose an adequate completion for distributive nearlattices. We give a proof of the existence of such a completion...
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Interpolation Pseudo-Ordered Algebras Over Partially Ordered Fields
Characteristics of partially pseudo-ordered ( K -ordered) algebras over partially ordered fields are considered. Properties of the set L ( A ) of all...
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Which Distributive Lattices are Lattices of Open Sets of P-Spaces?
Representing lattices by topologies has been studied to a great extent. In this paper, we prove that a complete lattice L is isomorphic to the...
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Strongly Algebraically Closed Cevian Lattices
AbstractCevian operations on certain distributive lattices with zero were introduced by F. Wehrung in 2019, and they have been intensively studied...
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Interpolation Pseudo-Ordered Rings
Characteristics of partially pseudo-ordered ( K -ordered) rings are considered. Properties of the set L ( R ) of all convex directed ideals in...
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Unitless Frobenius Quantales
It is often stated that Frobenius quantales are necessarily unital. By taking negation as a primitive operation, we can define Frobenius quantales...
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The Gumm level equals the alvin level in congruence distributive varieties
Congruence modular and congruence distributive varieties can be characterized by the existence of sequences of Gumm and Jónsson terms, respectively....
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Causal structure of spacetime and Scott topology
In this paper we establish the spacetime manifold as a partially ordered set via the casual structure. We show that these partially ordered sets are...
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Cancellable Elements in the Lattice of Overcommutative Semigroup Varieties
We completely determine all cancellable elements in the lattice \(\mathbb {OC}\)...
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Equivalence à la Mundici for commutative lattice-ordered monoids
We provide a generalization of Mundici’s equivalence between unital Abelian lattice-ordered groups and MV-algebras: the category of unital commutative...
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Free Vector Lattices and Free Vector Lattice Algebras
We show how the existence of various free vector lattices and free vector lattice algebras can be derived from a theorem on equational classes in...
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Characterizations of the projection bands and some order properties of the lattices of continuous functions
We show that for an ideal H in an Archimedean vector lattice F the following conditions are equivalent:
H is a projection band;
Any collection of...
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On the number of atoms in three-generated lattices
As the main result of the paper, we construct a three-generated, 2-distributive, atomless lattice that is not finitely presented. Also, the paper...
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Total coloring of graphs associated with algebraic structures and ordered structures
In this paper, we prove that the zero-divisor graphs of finite posets and the complement of zero-divisor graphs of finite 0-distributive posets...
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The Distinguishing Number and Distinguishing Chromatic Number for Posets
In this paper we introduce the concepts of the distinguishing number and the distinguishing chromatic number of a poset. For a distributive lattice L ...