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On Lattice Vector Spaces over a Distributive Lattice
In this paper, we show a homomorphism between lattices that induces a lattice vector space over a distributive lattice. The notion of congruence...
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Distributive and Lower-Modular Elements of the Lattice of Monoid Varieties
In the lattice of semigroup varieties, the set of all neutral elements is finite, the set of all distributive elements is countably infinite, and the...
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Varieties of aperiodic monoids with central idempotents whose subvariety lattice is distributive
We completely classify all varieties of aperiodic monoids with central idempotents whose subvariety lattice is distributive.
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Chain algebras of finite distributive lattices
We introduce a family of toric algebras defined by maximal chains of a finite distributive lattice. Applying results on stable set polytopes, we...
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Filter Classes of Upsets of Distributive Lattices
Let us say that a class of upward closed sets (upsets) of distributive lattices is a finitary filter class if it is closed under homomorphic...
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Representing Distributive Dually Algebraic Lattices
We show that every distributive dually algebraic lattice can be represented as Sp(S, H) with S an algebraic lattice and H a monoid of operators. As a...
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Lattice-ordered pregroups are semi-distributive
We prove that the lattice reduct of every lattice-ordered pregroup is semidistributive. This is a consequence of a certain weak form of the...
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Multiple knapsack-constrained monotone DR-submodular maximization on distributive lattice
We consider a problem of maximizing a monotone DR-submodular function under multiple order-consistent knapsack constraints on a distributive lattice....
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The First Syzygy of Hibi Rings Associated with Planar Distributive Lattices
In this article, we give explicit minimal generators of the first syzygy of the Hibi ring for a planar distributive lattice in terms of sublattices....
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Subordinations on Bounded Distributive Lattices
In this paper we shall study some classes of bounded distributive lattices endowed with a subordination relation, called subordination lattices. We...
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Absolute Retracts for Finite Distributive Lattices and Slim Semimodular Lattices
Let n denote a positive integer. We describe the absolute retracts for the following five categories of finite lattices: (1) slim semimodular...
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Two Flags in a Semimodular Lattice Generate an Antimatroid
A basic property in a modular lattice is that any two flags generate a distributive sublattice. It is shown (Abels 1991, Herscovici 1998) that two...
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Associative Algebras with a Distributive Lattice of Subalgebras
We give a full description of associative algebras over an arbitrary field, whose subalgebra lattice is distributive. All such algebras are...
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Canonical extensions, free completely distributive lattices, and complete retracts
We provide a simple proof of a recent result of Morton and van Alten that the canonical extension of a bounded distributive lattice is its free...
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On Permutation Distributive BI-Algebras
The purpose of this work is to introduce permutation BI-algebras as a new class of algebras in order to understand how it interacts to existing...
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