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On Convex Directed Subgroups of Pseudo Lattice-Ordered Groups
We show that all convex directed subgroups of a pl -group form a distributive lattice under inclusions that is a Brouwer lattice. We succeeded in...
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Length-preserving Extensions of a Semimodular Lattice by Lowering a Join-irreducible Element
We extend the bijective correspondence between finite semimodular lattices and Faigle geometries to an analogous correspondence between semimodular...
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Cartesian Lattice Counting by the Vertical 2-sum
A vertical 2-sum of a two-coatom lattice L and a two-atom lattice U is obtained by removing the top of L and the bottom of U , and identifying the...
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General Mixed Lattices
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice...
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Multiplicatively Idempotent Semirings with Annihilator Condition
Abstract—The structural theory of semirings with additional conditions is considered. Multiplicatively idempotent semirings with the annihilator...
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Adjunction of a strong unit to a hyper-archimedean lattice-ordered group
This paper studies conditions in which a hyperarchimedean lattice-ordered group embeds into a hyperarchimedean lattice-ordered group with strong...
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Extremality, left-modularity and semidistributivity
In this article we study the relations between three classes of lattices each extending the class of distributive lattices in a different way. In...
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On Nontrivial Weak Dicomplementations and the Lattice Congruences that Preserve Them
We study the existence of nontrivial and of representable (dual) weak complementations, along with the lattice congruences that preserve them, in...
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The Lattice NExtS41 as Composed of Replicas of NExtInt, and Beyond
We study the lattice of all normal consistent extensions of the modal logic...
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Complexity of the universal theory of bounded residuated distributive lattice-ordered groupoids
We prove that the universal theory and the quasi-equational theory of bounded residuated distributive lattice-ordered groupoids are both
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Minimal representations of a finite distributive lattice by principal congruences of a lattice
Let the finite distributive lattice D be isomorphic to the congruence lattice of a finite lattice L . Let Q denote those elements of D that correspond...
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Interpretation of Skew Ideals with Relators in Join Skew Semilattice
Distributive semilattices must be the foundation of algebraic subjects related to nonclassical logic. An ideal topic for reviewing the order...
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On a Convex Geometric Connection to Threshold Logic
A convex geometric connection to Threshold Logic will be reviewed. We have presented necessary and sufficient conditions to recognize cut-complexes...
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Affinely representable lattices, stable matchings, and choice functions
Birkhoff’s representation theorem (Birkhoff, Duke Math J 3(3):443–454, 1937) defines a bijection between elements of a distributive lattice and the...
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Spectral properties of cBCK-algebras
In this paper we study prime spectra of commutative BCK-algebras. We give a new construction for commutative BCK-algebras using rooted trees, and...
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The L-fuzzy vector subspace degrees and its induced convex structure
This study aimed to investigate the degree to which an L -fuzzy subset of a vector space could be considered an L -fuzzy vector subspace....
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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...