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Characterizing representability by principal congruences for finite distributive lattices with a join-irreducible unit element
For a finite distributive lattice D , let us call Q ⊆ D principal congruence representable , if there is a finite lattice L such that the congruence...
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The congruence frame and the Madden quotient for partial frames
Nuclei and prenuclei have proved popular for providing quotients in frame theory; moreover the collection of all nuclei is itself a frame with useful...
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Homomorphisms and principal congruences of bounded lattices I. Isotone maps of principal congruences
Two years ago, I characterized the order Princ L of principal congruences of a bounded lattice L as a bounded order.
If K and L are bounded lattices...
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Characterizing fully principal congruence representable distributive lattices
Motivated by a recent paper of G. Grätzer, a finite distributive lattice D is called fully principal congruence representable if for every subset Q ...
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Natural congruences and isomorphism theorems for directed complete partially ordered sets
Directed complete partially ordered sets (dcpos, for short) play an important role in domain theory. The aim of this paper is to characterise natural...
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Complete congruence lattices of two related modular lattices
By a 1991 result of R. Freese, G. Grätzer, and E. T. Schmidt, every complete lattice A is isomorphic to the lattice Com( K ) of complete congruences of...
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Congruences of fork extensions of slim, planar, semimodular lattices
For a slim, planar, semimodular lattice L and a covering square S of L , G. Czédli and E. T. Schmidt introduced the fork extension, L [ S ], which is...
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An independence theorem for ordered sets of principal congruences and automorphism groups of bounded lattices
For a bounded lattice L , the principal congruences of L form a bounded ordered set Princ( L ). G. Grätzer proved in 2013 that every bounded ordered set...
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Representing some families of monotone maps by principal lattice congruences
For a lattice L with 0 and 1, let Princ( L ) denote the set of principal congruences of L . Ordered by set inclusion, it is a bounded ordered set. In...
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Congruences in slim, planar, semimodular lattices: The Swing Lemma
In an earlier paper, to describe how a congruence spreads from a prime interval to another in a finite lattice, I introduced the concept of...
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On semicontinuous lattices and their distributive reflections
In this paper, we are mainly concerned with semicontinuity of complete lattices and their distributive reflections, introduced by Rav in
1989 . We... -
Existence and Regularity Results for Fully Nonlinear Operators on the Model of the Pseudo Pucci’s Operators
This paper is devoted to the existence and Lipschitz regularity of viscosity solutions for a class of very degenerate fully nonlinear operators, on...
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Congruences and prime-perspectivities in finite lattices
In a finite lattice, a congruence spreads from a prime interval to another by a sequence of congruence-perspectivities through intervals of arbitrary...
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On a result of Gábor Czédli concerning congruence lattices of planar semimodular lattices
A planar semimodular lattice is slim if it does not contain M 3 as a sublattice. An SPS lattice is a slim, planar, semimodular lattice. Congruence...
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Representing a monotone map by principal lattice congruences
For a lattice L , let Princ ( L ) denote the ordered set of principal congruences of L . In a pioneering paper, G. Grätzer proved that bounded ordered...
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Grain Boundary Migration with Thermal Grooving Effects: A Numerical Approach
Grain boundary migration in the presence of thermal grooving effects play a critical role in the stability of the thin polycrystalline films used in...